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i

Acknowledgement

I still remember the day when I arrived in Finland for the first time. It was in the autumn of the year 2000 and I came to Finland with my dream of studying in this mystical far northern land. Time flies! During these 16 years I have stud-ied subjects as diverse as environmental science, information technology, ap-plied mathematics and more. Finally, I will soon become a doctor in the field of Geoscience. Life is full of surprises!

This doctoral dissertation wouldn´t have been successful without the help of many people. First of all, I am deeply grateful to my supervising Professor Kirsi Virrantaus for her important and irreplaceable role in my doctoral work. She recruited me to her academic world and provided me with opportunities to join different types of research projects. She provided me with guidance, knowledge, and the expertise that I needed during my research and also encouraged me whenever I was having difficulties.

I would like to thank Dr. Urska Demsar, my instructor at the School of Geog-raphy and Geosciences, University of St. Andrews. She has been the co-author of my journal articles where she provided me with the spirit of innovative think-ing as well as many valuable comments and a lot of important advice regarding scientific writing. I am also very thankful to Dr. Paula Ahonen-Rainio who has been teaching me visualisation and GIS courses during my masters´ and PhD studies. I also thank Prof. Vesa Niskanen who brought fuzzy logic to my research work and provided much help in fuzzy modelling. I want to thank my colleagues Jaakko and Rangsima, who always provided me with helpful and friendly dis-cussions when I had some problems during my research. I also want to thank my colleagues Jari and Salla for being good company during my con-ference trips. My thanks belong to Jussi, Pekka, Jari and Hannes for their good cooper-ation during the research projects. I want to thank my colleagues Andreas and Antti for being a friendly neighbour in my office and Jaana who has been shar-ing the experience of decision making in my research.

I am grateful to the Finnish Academy of Finland, Finnish Funding Agency for Innovation (Tekes), Finnish Transport Agency, The Finnish Defence Forces, and the National Emergency Supply Agency for funding my research. In partic-ular, I want to thank those experts at Technical Research Centre of Finland Ltd (VTT), the Finnish Meteorological Institute, Caruna Ltd, the University of East-ern Finland, the Emergency Service College, InstaDefSec, Erillisverkot and the Water and Environmental Engineering Laboratory of Aalto University for their fruitful co-operation in the research projects. I am grateful to my thesis pre-

ii

examiners, Professor Tao Cheng and Professor Alfred Stein for their valuable comments. I also thank Professor Tao Cheng and Professor Christophe Clara-munt for acting as my opponents.

Finally, my biggest thank belongs to my parents who raised me up as a smart and independent girl. They provided me with the opportunity to come to Fin-land, and passed on to me the spirit of hard working and ambition. They always make me feel loved! I also want to remember and thank my grandma Xiu Yun Gao who passed away in the year 2001. I want to thank my husband Tuomo, who always supports me, for being with me during all these years. My sweet thanks belong to my daughters Sanni who designed the cover picture of my dis-sertation and Aini, for always warming up my heart with their cute smiles.

Espoo, 17. 09.2016 Zhe Zhang

iii

List of Publications

This doctoral dissertation consists of a summary and of the following publica-tions which are referred to in the text by their numerals 1. Zhang, Zhe; Rangsima, Sunila; and Virrantaus, Kirsi (2010). A spatio-tem-poral population model for alarming, situational picture and warning system. Guilbert E., Lees B., Leung Y., eds., In: Proceeding joint international confer-ence on theory, data handling and modeling in geospatial information sci-ence, 2010, The International Archives of the Photogrammetry, Remote sens-ing and Spatial Information Sciences, 38 (2), 69-74.

2. Zhang, Zhe and Virrantaus, Kirsi (2010). Analysis of vulnerability of road networks on the basis of graph topology and related attribute information. Philips-Wren G., Jain L. C., Nakamatsu K., Howlett R., eds., In: proceeding of the second KES international symposium IDT 2010, Advances in Intelligent Decision Technologies, New York: Springer Berlin Heidelberg, 353-363.

3. Zhang, Zhe; Demšar, Urška; Rantala, Jaakko; and Virrantaus, Kirsi (2014). A fuzzy multiple-attribute decision making modelling for vulnerability analysis on the basis of population information for disaster management. International Journal of Geographical Information Science, 28(9), 1922-1939.

4. Zhang, Zhe and Virrantaus, Kirsi (2016). Use of fuzzy decision-making ap-proach in an analysis of the vulnerability of street networks for disaster man-agement. Nordic Journal of Surveying and Real Estate Research. (Accepted)

5. Zhang, Zhe; Demšar, Urška; and Virrantaus, Kirsi (2016). A spatial fuzzy in-fluence diagram for modelling spatial objects dependencies: a case study on tree-related electricity outages. International Journal of Geographical Infor-mation Science. ( submitted)

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Author’s Contribution

A spatio-temporal population model for alarming, situational picture and warning system. The author had the main responsibility of planning and implementing the re-search, analysing the results and wrote the article. Dr. Rangsima Sunila re-viewed and commented on the article. Prof. Kirsi Virrantaus acted as supervi-sor of the research, reviewed and commented the article.

Analysis of vulnerability of road networks on the basis of graph topology and related attribute information. The author had the main responsibility of planning and implementing the re-search, analysing the results and wrote the article. Prof. Kirsi Virrantaus acted as supervisor of the research, reviewed and commented the article.

A fuzzy multiple-attribute decision making modelling for vul-nerability analysis on the basis of population information for disaster manage-ment.

The author had the main responsibility of planning and implementing the re-search, analysing the results and wrote the article. Prof. Kirsi Virrantaus acted as supervisor of the research work, reviewed and commented on the article. Dr. Urška Demšar acted as instructor, reviewed and commented on the article. Mr. Jaakko Rantala reviewed and commented on the article.

Use of fuzzy decision-making approach in an analysis of the vul-nerability of street networks for disaster management. The author had the main responsibility of planning and implementing the re-search, analysing the results and wrote the article. Prof. Kirsi Virrantaus acted as supervisor of the research, reviewed and commented on the article.

A spatial fuzzy influence diagram for modelling spatial objects dependencies: a case study on tree-related electricity outages. The author had the main responsibility of planning and implementing the re-search, analysing the results and wrote the article. Prof. Kirsi Virrantaus acted as supervisor of the research work, reviewed and commented on the article. Dr. Urška Demšar acted as instructor, reviewed and commented on the article.

v

List of Abbreviations and Symbols

FMI Finnish Meteorological Institute

MAVT Multiple attribute value theory

SMART Simple multi-attribute rating technique

MADM Multiple attribute decision making

MCDM Multi-criteria decision making

MAUT Multi-attribute utility theory

MF Membership function

Digiroad National road and street database

GIScience Geographical Information Science

SFID Spatial fuzzy influence diagram

SDSS Spatial decision support system

vi

Contents

Acknowledgement ..................................................................................... i

List of Publications ................................................................................. iii

Author’s Contribution ............................................................................. iv

List of Abbreviations and Symbols........................................................... v

List of Figures ........................................................................................ viii

List of Tables ........................................................................................... ix

1. Introduction .................................................................................. 1

1.1 Background and motivation ...................................................... 1

1.2 Key concepts .............................................................................. 2

1.3 Related research ........................................................................ 4

1.3.1 Vulnerability of critical infrastructure ...................................... 5

1.3.2 Population information modelling ........................................ 5

1.3.3 Multi-criteria decision making .............................................. 6

1.3.4 Influence diagram .................................................................. 7

1.4 Objective and research questions ............................................. 8

2. Theoretical foundation ................................................................ 12

2.1 Spatio-temporal modelling ...................................................... 13

2.2 Decision making ...................................................................... 15

2.2.1 Multiple attribute value theory ............................................ 15

2.2.2 Fuzzy multiple attribute decision making ........................... 16

2.2.3 Influence diagram ................................................................ 18

2.3 Graph Theory and Centrality measures .................................. 19

3. Research methods and materials ................................................ 21

4. Research results .......................................................................... 34

4.1 Role of population information in disaster management. ...... 34

4.1.1 Spatio-temporal population model ......................................... 35

vii

4.2 Spatial decision models for vulnerability analysis of road network 37

4.2.1 Crisp multiple attribute value theory decision model ......... 37

4.2.2 Fuzzy multiple attribute decision making model ................ 39

4.2.3 Model the complexity and uncertainty of population information in disaster management .......................................................................... 41

4.3 Analysis of vulnerability of electricity network in a case of tree-related outages ............................................................................................... 44

5. Discussion ................................................................................... 46

5.1 Spatio-temporal population model ......................................... 46

5.2 Multi-criteria decision model ................................................. 47

5.3 Modelling spatial objects´ dependency .................................. 48

5.4 Future work ............................................................................. 48

6. Conclusion ................................................................................... 51

References.............................................................................................. 52

viii

List of Figures

Figure 1 Interconnection between the vulnerability of critical infrastructure and key theories. ....................................................................................................................... 13 Figure 2 Example of bitemporal element. Modified from Worboys (1994). ............... 15 Figure 3 An example of fuzzy MFs and fuzzy rules. ...................................................... 17 Figure 4 Structure of influence diagram. ..................................................................... 19 Figure 5 Illustration of method. ................................................................................... 22 Figure 6 Illustration of SWING weighting method. ...................................................... 25 Figure 7 Fuzzy MFs for input attributes. ...................................................................... 27 Figure 8 Gaussian MFs of input attributes. .................................................................. 30 Figure 9 Illustration of fuzzy rules. ............................................................................... 30 Figure 10 General structure of spatial fuzzy influence diagram. ................................. 31 Figure 11 Spatial fuzzy influence diagram in modelling tree-related electricity outages. ........................................................................................................................ 33 Figure 12 Role of population information in disaster management. ........................... 35 Figure 13 Spatio-temporal population model software user interface. ...................... 36 Figure 14 An overall value map for the first application by using SWING weighting method. ........................................................................................................................ 37 Figure 15 Normalised population size map. ................................................................. 38 Figure 16 Normalised betweenness attribute map. .................................................... 38 Figure 17 Normalised cut edge attribute map. ............................................................ 38 Figure 18 An overall value map for the second application by using SMART weighting method. ........................................................................................................................ 39 Figure 19 Vulnerability map of road network. ............................................................. 40 Figure 20 Population size attribute map. ..................................................................... 40 Figure 21 Betweenness attribute map. ........................................................................ 40 Figure 22 Kernel density map of population information by using fuzzy model normalised results. ........................................................................................................ 42 Figure 23 Kernel density map of population information by using normalised population size attribute values. ................................................................................... 43 Figure 24 Kernel density map of population information by using normalised number of children attribute values. .......................................................................................... 43 Figure 25 Vulnerability map of electricity network in a case of tree-related outages. 45

ix

List of Tables

Table 1 Spatial decision problems related with vulnerability analysis of critical infrastructure in disaster management. ........................................................................ 9 Table 2 Summary of the research articles. .................................................................. 21 Table 3Population size estimation methods for 11 spatio-temporal objects. ............ 23 Table 4 Illustration of MAVT and overall value calculation methods. ......................... 25 Table 5 Weights for the corresponding attributes in the case the vulnerability analysis of a road network for the preparedness against a terrorist attack. ............................ 25 Table 6 Weights for the corresponding attributes in the case the vulnerability analysis of a road network for preparedness for rescue in the event of a terrorist attack. ..... 26 Table 7 Ranks of combinations of MFs from experts, demonstrating the antecedent and consequent part of the fuzzy rules. H: high M: middle L: low. For example, HPHC

refers to high (a large) number of people and children live inside a building. ........... 27 Table 8 Example of using fuzzy set accuracy assessment to validate the fuzzy model´s result. n=3, m=6, AND C= {HP, MP, LP, HC, MC, LC}. The columns HP, MP, LP, HC, MC, LC form the 63 matrix A. ................................................................................................ 29 Table 9 Validation of the fuzzy model by using fuzzy set accuracy assessment and domain knowledge of rescue expert. Hp: high number of people, MP: Middle number of people, LP: low number of people, Hc: high number of child, Mc: Middle number of child, Lc: low number of child...................................................................................... 44

1

1. Introduction

1.1 Background and motivation

Natural and man-made hazards, disasters, and concerns such as the increasing amount of terrorism, cause insecurity for people and society. Critical infrastruc-ture plays an important role in supporting society and human life, and also in responding to such disasters.

Natural disasters cause huge damage to infrastructure, as well as associated industries and loss of life of those that were relying on the infrastructure. Dur-ing the last decade, China and the United States were the countries that experi-enced the most disasters by population density. For instance, flooding caused the majority of disasters, accounting for 43% of all recorded events and affecting nearly 2.5 billion people. Storms were the second most frequent type, killing more than 244,000 people and costing $936 billion US dollars in recorded dam-ages (CRED, 2015). One of the main reasons for fatalities and financial loss is the inadequacy of critical infrastructure to withstand the cataclysmic effects of natural disasters and the lack of mitigation strategies and preparedness, when they occur on the part of emergency services, disaster relief agencies, industries and communities. If the vulnerable locations of the critical infrastructure can be identified and reinforced in advance, the damage and impact can be signifi-cantly reduced.

Much effort in critical infrastructure vulnerability analysis has been focused on developing models to simulate the behavior of critical infrastructure systems and to discover the interdependencies of the infrastructure systems (Pederson 2006, Chang et al. 2007, Espada et al. 2015, Utne et al. 2011, McDaniels et al. 2007). However, most of the methods focus on critical infrastructure functional dependency, without considering the topological dependency and spatial con-text. Uncertainty of the information as well as population information, were of-ten ignored in the modelling process.

Often disasters are not only the natural events that cause them, they are the product of social, political and economic environments because of the way these structures are constructed by different groups of people. Therefore, disasters are a complex mix of natural hazards and human actions (Wisner et al., 2004). In the event of a disaster, population information can also play an important role. For instance, the location information of victims can help rescue personnel to prioritise the area and maximise rescue resources and efficiency. Population information can be also used to help decision makers (DMs) to locate rescue

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resources to aid in effective transportation and evacuation. The traditional way of modelling population information is by visualising the population density for example by using a kernel density map (Špatenková and Stein 2010, Krisp and Karasová 2005). However, those methods can only represent the static location of the people and other relevant demographic information, such as age, educa-tional background, and health are not taken into account and may be relevant to the rescue operation. On the other hand, another problem which is related to population information modelling is how to model population dynamics, be-cause people invariably move to different locations over time.

The analysis of networks is often based on traditional graph analysis. For in-stance, the shortest path algorithm is often used for analysing the functionality of transportation networks (Zhan 1997, Manley et al. 2015). If critical infrastruc-ture such as road networks and electricity networks can be modelled as spatial networks, the vulnerability analysis should not only be based on the topological structure of the network; some non-topological attributes such as population information, should also be considered. Moreover, experts' knowledge, which acts as one of the most important decision-making parameters, is often difficult to collect and represent, which causes the imprecision of the model compared to the real world domain. Therefore, there is a need to explore new methodology to solve the above mentioned problems.

The objective of this research is to develop several computational methods in supporting spatial decision making in analysis of vulnerability of critical infra-structure for disaster management. Most of the methods use population infor-mation as one of the parameters and take vagueness of the classification into consideration in the modelling process.

1.2 Key concepts

Critical infrastructure: Marsh (1998), provides the first definition of infra-structure as “a network of independent, mostly privately-owned, man-made systems that function collaboratively and synergistically to produce and distrib-ute a continuous flow of essential goods and services. “ A critical infrastructure is “an infrastructure so vital that its incapacity or destruction would be a debili-tating impact on our defence and national security”. The definition has grown out of an earlier definition that includes only 5 sectors, and today's definition of critical infrastructure includes 11 sectors: agriculture and food, water, public health, emergency services, defence, industrial base, telecommunications, en-ergy, transportation, banking and finance, chemical and hazardous materials and postal services and shipping. The key assets are: national monuments and icons, nuclear power plants, dams, government facilities, and important com-mercial assets (Lewis 2006).

Vulnerability: Many of the discrepancies in the definition of vulnerability arise from different epistemological orientations and subsequent methodologi-cal practices. In general, vulnerability studies can be categorised into three themes, 1) vulnerability as risk/hazard exposure; 2) vulnerability as social re-sponse: 3) vulnerability of places (Cutter 1996). The first research theme focuses

3

on the distribution of hazardous conditions where vulnerability is described as the degree of loss associated with the occurrence of the hazard event (Cutter 1996). The second theme highlights the social construction of vulnerability; a condition of historical social and economic processes that impinges on the indi-vidual´s or society´s ability to cope with disasters and adequately respond to them. The third research theme is more geographically centred, which means vulnerability is both a biophysical risk as well as a social response within a spe-cific area or geographic domain (Cutter 1996). There are several definitions that can be found. Timmerman (1981) define vulnerability as “Vulnerability is the degree to which a system acts adversely to the occurrence of a hazardous event. The degree and quality of the adverse reaction are conditioned by a system's resilience (a measure of the system's capacity to absorb and recover from the event)”. Dow (1992) define vulnerability as “Vulnerability is the differential ca-pacity of groups and individuals to deal with hazards, based on their positions within physical and social worlds.”

Disaster management: Disasters is a serious disruption of the functioning of a community or a society involving widespread human, material, economic or environmental losses and impacts, which exceeds the ability of the affected community or society to cope using its own resources (UNISDR 2009). There are four phases which used to describe disaster management, 1) mitigation 2) preparedness 3) response and 4) recovery (Cova 1999; UNISDR 2009). The mit-igation phase is defined as ‘the lessening or limitation of the adverse impacts of hazards and related disasters’, whereas the preparedness phase is defined as ‘the knowledge and capacities developed by governments, professional response and recovery organisations, communities and individuals to effectively anticipate, respond to, and recover from, the impacts of likely, imminent or current hazard events or conditions’ (UNISDR 2009). The response phase is further defined as ‘the provision of emergency services and public assistance during or immedi-ately after a disaster in order to save lives, reduce health impacts, ensure public safety and meet the basic subsistence needs of the people affected’, whereas the recovery phase is defined as ‘the restoration, and improvement where appropri-ate, of facilities, livelihoods and living conditions of disaster-affected communi-ties, including efforts to reduce disaster risk factors’ (UNISDR 2009).

Spatial information and Geographical Information Science (GIS): Spatial data links a geographic location (place), often a time, and some descrip-tive property or attribute of the entity. Spatial information is spatial data that has been given a meaning in a certain context or processed from spatial data in order to be useful (Fisher 2011). GIS is a special class of information science that keeps track not only of events and activities, but also of where they happen or exist. It is a computerised tool for solving geographic problems and used for the storage, retrieval and display of geographical information (Longley et al. 2005, Goodchild 2010). Spatial analysis is “a general ability to manipulate spatial data into different forms and extract additional meaning as a result” (Bailey 1994).

Spatial decision making: All decision-making involves making a choice from a set of alternatives in a situation of uncertainty. Each problem is unique

4

and contains its own particular difficulties. Therefore, a decision-making anal-ysis process needs to take place. Decision-making problems that involve geo-graphical data are referred to as geographical or spatial decision problems (Mal-czewski 1999). Spatial decision-making refers to the decision-making process which a decision-maker has to face with a complex spatial problem which has multiple, conflicting, objectives. Here, data is regarded as geographical if it can be associated with a place or location.

A spatial decision support system (SDSS) is designed to support the decision-making process for complex spatial problems. It provides a framework for inte-grating analytical and spatial modelling capabilities, spatial and non-spatial data management, domain knowledge, spatial display capabilities and reporting capabilities (Sugumaran and Degroote 2011, Densham 1991). A spatial decision support system is used to help decision-makers to overcome the difficulties which arise in the decision-making process. The source of difficulties in making decisions commonly arise from complexity, uncertainty, multiple objectives and competing viewpoints(Clemen and Reilly 2013).

Uncertainty of the geographical information: The uncertainty of geo-graphical information is one of the most important issues in spatial decision-making. Any collection of observational geographical information is prone to uncertainty in a number of forms. For instance, uncertainty can be the problem of defining the class of object to be examined or individual objects to be ob-served, property to be measured and errors during the processing of these ob-servations. Fisher (2006), introduced a conceptual model of uncertainty in spa-tial data. The class, or individual objects can be described as well or poorly de-fined. If the objects are well defined, then the uncertainty is caused by errors and it’s probabilistic in nature. If the object is poorly defined, then the definition of a class or set within the universe is a matter of vagueness or ambiguity which can be treated by using fuzzy set theory (Fisher 2006). Decision-makers can use analytical modelling techniques to enhance decision-making capabilities and in dealing with uncertainty.

1.3 Related research

This chapter introduces recent studies from both theoretical and application do-mains. Section 1.3.1 focuses on a survey of the literature concerning the vulner-ability analysis of critical infrastructure. It starts with a general overview of dif-ferent types of methods used in modelling the vulnerability of critical infrastruc-ture. Later, it presents a few examples from the literature which used fuzzy logic to solve the problem of the uncertainty of classification used in vulnerability analysis. Section 1.3.2 introduces various types of population models and pop-ulation information data sources. Multi-criteria decision analysis (MCDM) is one of the core methods used in the research. Related literature which uses MCDM decision analysis is presented in 1.3.3. Section 1.3.4 introduces a survey of the literature which is related to influence diagrams.

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1.3.1 Vulnerability of critical infrastructure

Critical infrastructure includes several sectors that are interconnected with each other at multiple levels (Chang et al., 2007; Galbusera et al. 2015; Hernandez-Fajardo and Dueñas-Osorio 2013; Lewis, 2006; Utne et al. 2011, McDaniels 2007). Much research has been done to model the vulnerability of critical infra-structure in the case of disaster management. Ouyang (2013), has made a review of the literature on modelling and a simulation of an interdependent critical in-frastructure system. The literature can be categorised as simulation based mod-els, graph based models, risk-management models and mathematical models.

In the category of simulation models, various types of simulation techniques are used to simulate the critical infrastructure interdependencies and function failures (Porcellinis et al. 2008, Price and Vojinovic 2008). In graph based model, Demšar et al. (2008) uses a set of graph centrality measures to analyse the vulnerability of road networks on the basis of a network´s topological struc-ture. Jenelius et al. (2005), presents a link importance and site exposure ap-proach to measure road network vulnerability. Holmgren (2006), used a graph model to analyse the vulnerability of electric power networks.

Examples of risk management models include Ezell et al.'s (2000), probabil-istic risk-analysis model for water supply and treatment systems, Koonce et al.'s (2008), risk-analysis model for Bulk power systems. In the category of mathe-matical models, Guikema (2009) introduced a statistical learning theory model for analysing the probability or consequences of critical infrastructure system failure. Another approach includes Church et al.'s (2008), spatial optimisation model which can be used to identify the most critical facility assets in a service and supply system. Brown et al. (2005), uses a Bi-level program MAX-MIN to analyse the vulnerability of critical infrastructure in the case of a terrorist attack.

It is the case, however, that the difficulties that arise in interpreting the vul-nerability of critical infrastructure can be caused by vagueness of parameters´ classification. Despite the availability of research on this issue, the nature of the problem additionally requires the utilisation of fuzzy logic in order to deal with the vagueness of the decision environment in practice. Akgun et al. (2009), uses fuzzy integrated vulnerability assessment to model the vulnerability of an air-port in the case of terrorism. EI Rashidy and Grant-Muller (2013) introduced a link vulnerability indicator which is based on fuzzification and an exhaustive search optimisation technique to compute the vulnerability of road transporta-tion networks.

1.3.2 Population information modelling

Population information plays an important role in defining vulnerability for natural-hazard and disaster-management (Lewis 1999, Wisner et al. 2004). Deichmann (1996) gave an overview on spatial population database design and modelling. There are two data sources that are often used to model population information.

The first source is by using census data and results which are represented as various types of population density maps. For instance, Krisp and Karasová

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(2005) used population density maps to support fire and rescue operations in the Helsinki area. Špatenková and Stein 2010 applied statistical point pattern analysis to explore the causes of domestic fires based on population and build-ing information. Another similar study is Tillander et al.'s (2010) comparison of statistical risk models to spatial risk models in order to predict accident rates in Finland. Wu et al. (2004), developed a vulnerability map for risk assessment on the basis of various natural factors and population information. Mennis (2003), uses dasymmetric mapping combined with census data to generate a surface based representation of population.

Another way of modelling people´s location is by using mobile phone data. For instance, Bengtsson et al. (2011), used position data of subscribers' identity module (SIM) cards from a mobile phone company to estimate the magnitude and trends of population movements following the Haiti 2010 earthquake and cholera outbreak. González et al. (2008) studied the trajectory of 100,000 anon-ymised mobile phone users to map individual human mobility patters. How-ever, spatially detailed changes across scales of time are difficult to assess and limit the application of human population maps in situations in which timely information is required. In the field of dynamic population mapping, Deville et al. (2014) introduced dynamic population mapping by using mobile phone data where detailed maps of national population distribution during any time period are presented as results.

1.3.3 Multi-criteria decision making

Many spatial decision problems are related to the GIS-based MCDM decision analysis (GIS-MCDA). These two distinctive areas of research, GIS and MCDA, can be combined and are mutually beneficial (Malczewski 1999, Thill 1999, Chakhar and Martel 2003). Indeed, GIS is often recognised as a decision sup-port tool capable of performing spatial analysis in many problematic decision-making scenarios. A variety of GIS analytical techniques have been developed to help decision-makers to solve spatial decision-making problems with multi-ple criteria. Malczewski (2006), categorized the GIS-based multiple-criteria de-cision-making (GIS-MCDM) analyses into two categories: decisions under con-ditions of certainty and uncertainty. According to Malczewski (2006), the de-terministic approaches were presented in 263 papers or approximately 77% of the total and the rest of the research on the GIS-MCDA under conditions of un-certainty. Of the 78 articles on decision problems under conditions of uncer-tainty, 35.9% fall into the probabilistic decision analysis category and 64.1% of the articles were found to represent fuzzy decision-making.

One of the major application areas is found to be in environmental science (Tuzkaya et al. 2009, Greening and Bernow 2004, Hermann et al. 2007). For instance, Huang et al. (2011) made a survey of the literature using multi-criteria decision analysis in environmental management. The application area includes hydrology and water resources management applications (Makropoulos et al. 2003, Chowdhury and Rahman 2008), waste management applications (Kapepula et al. 2007, Khan and Faisal 2008, Hung et al. 2007) and agriculture and forestry (Morari et al. 2004, Ananda and Herath, 2009).

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Few literary sources can be found to use MCDM to model critical infrastruc-ture. The methods are observed to be popular in energy planning followed by energy resource allocation (Afgan and Carvalho 2002, Wang et al. 2009) and transportation (Fuller et al. 2003, Jakimavičius and Burinskiene 2009, Can-tarella and Vitetta 2006). In the field of disaster management, Rashed and Weeks (2003) combined an MCDM analysis approach with fuzzy modelling to assess the vulnerability analysis of an urban area in the modelling of an earth-quake hazard. Opricovic and Tzeng (2002) applied fuzzy MCDM to solve the problem concerning post-earthquake reconstruction including the restoration of critical infrastructure such as electricity, water and transportation networks. Apostolakis and Lemon (2005), used Multi-Attribute Utility Theory (MAUT) for the identification and prioritisation of vulnerabilities in an infrastructure by us-ing interconnected diagrams and employed graph theory to identify the candi-date vulnerable scenarios. Ezell (2007) proposed an Infrastructure Vulnerabil-ity Assessment Model (I-VAM) based on MAUT and applied it to a medium-sized clean water system. Catrinu and Nordgård (2010) integrated risk analysis and multi-criteria decision support under uncertainty in a study of electricity distribution system asset management.

1.3.4 Influence diagram

Influence diagram is graphical representation of decision problem by using arcs and nodes. The most commonly used methods for evaluating the uncertainty of the nodes in the influence diagram are based on probabilities where the values of a node in an influence diagram are often represented as probabilities by using Bayesian Theorem (Neapolitan 2004), and the diagram is then called a Bayesian network. Bayesian networks are graphical probabilistic models which consist of a set of variables and their conditional dependencies (Jensen 1996, Aspinall 1992, Stassopoulou et al. 1998). Another way of modelling the uncertainty in an influence diagram is by using fuzzy logic. A fuzzy influence diagram models the uncertainty of a node by using fuzzy reasoning instead of probabilities. The use of fuzzy logic can overcome the difficulties associated with probability, which is especially useful when the node value cannot be assigned numerically or ex-pressed as probability (Mateou et al., 2005).

However, only a few references in the literature can be found to modelling spatial objects' dependencies. Zhu et al. (1996), modelled spatial object depend-encies as a knowledge based decision support system where a spatial influence diagram was used to support the decision making process of land use planning. In their work, they developed a land use spatial influence diagram software user interface, which can integrate GIS, expert knowledge, and other modelling tech-niques into the modelling process, and finally automate the solution process. Ezell et al. (2010), applied an influence diagram to determine the relative like-lihood of alternative types of terrorist attacks on the United States. Grêt-Re-gamey and Straub (2006) integrated Bayesian networks into a GIS analysis for supporting avalanche risk assessment.

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1.4 Objective and research questions

In this dissertation, four decision scenarios which are related to the vulnerabil-ity analysis of critical infrastructure in the case of disaster management are de-fined and illustrated in Table 1. The first two scenarios are related to how pop-ulation information can be used to support decision making in the case of an emergency. Population information is important, since saving people's lives is always the most important task in the rescue operation (Castrén et al., 2007). In this dissertation, we chose two types of critical infrastructure, transportation networks and electricity networks because they are two of the most important critical infrastructure for human society to function effectively. For instance, many other types of critical infrastructure such as telecommunication networks and water networks need electrical power in order to function. Transportation is needed for everyday life. It is also needed to evacuate the victims from endan-gered areas in disaster situations. Therefore, the third and fourth scenarios fo-cused on an analysis of the vulnerability of transportation and electricity net-works. With the decision-making problems and pertinent objectives established in the scenarios, various decision-making variables are discovered and four re-search questions are derived from them.

In all the decision-making scenarios, population information plays an im-portant role in defining vulnerability for disaster management. All man-made infrastructure is also intended to serve the general population. Therefore, the first research question should begin with the problems related with modelling population information for disaster management. It can be used to solve the first spatial decision problem: where are the victims and how much resources are needed to transport the inhabitants from the endangered area?

Moreover, each decision is made among at least two alternatives which are evaluated by using several decision variables. For instance, in spatial decision problems concerning which area rescue personnel should go to, the alternatives are several locations that rescue personnel are considering to go to first in order to reach the decision objective( see spatial decision problem II in Table 1). The decision variables which affect rescue personnel decision-making arise from several sources. The rescue personnel will thus not only consider the population density of the affected areas, but also the rescue time and individual character-istics of local populations, such as age, disabilities and/or health conditions, and how these variables affect the ability of individuals to deal with a disaster. Be-cause of the difficulties in combining all these different types of decision varia-bles, the decision-making process can be complex and time-consuming. There-fore, research question 2 was formulated, which related to making decisions un-der multivariate criteria.

Furthermore, research question 3 comes from the vagueness of classification in spatial decision-making. In order to identify the vulnerable locations of trans-portation and electricity networks (see spatial decision problem III and IV in table 1), we need to consider all the variables which could affect the vulnerability as well as the vagueness which relates to variable classification. For instance, it is difficult to say exactly what number of people living in a particular area con-stitute a high-risk area of a road network. This evaluation often depends on the

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implicit knowledge used in the decision-making process, which is difficult to quantify. Finally, the hard decisions can be caused by a complex relationship between spatial objects (critical infrastructure) which need to be modelled using advanced techniques. Research question 4 was thus formulated.

Table 1 Spatial decision problems related with vulnerability analysis of critical infrastructure in disas-ter management.

Spatial Decision Problems Decision objectives

Decision variables

I Where are the victims and how much resources are needed to transport the inhabitants from the endangered area?

-Maximizing rescue efficiency

-Population information -Time of the disaster -Accessibility of the risk area -Other potential vari-ables

II Which area rescue personnel should go first in order to save more lives?

-Maximizing rescue efficiency -Save more lives and resources

-Population information -Accessibility of the risk area, -Available rescue resources -Other potential vari-ables

III Which are the vulnerable loca-tions of the transportation net-work in a disaster situation?

-Minimizing the risk

-Population information -Network connectiv-ity -Spatial location - Other potential vari-ables

IV Where are the vulnerable loca-tions of the electricity network in the case of extreme weather conditions? How should we prepare for the disaster?

-Minimizing the risk of tree-related outages

-Population infor-mation -Electricity function failure -Spatial location of the network -Weather condition - Other potential vari-ables

Research question 1: How can population information be used in different phases of disaster management. How can population dynamics be modelled?

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The role of population information is essential in disaster management. Infor-mation relating to victims inside the risk area can help rescue personnel to esti-mate the resources needed to transport victims from the danger area and there-fore improve rescue efficiency. However, there have been many problems inher-ent in modelling population information. One of the problems is how to model population dynamics because people move to different places over time. This issue is especially important in disaster management, since a disaster is an event which occurs both in space and time, the number of people inside the risk area is dynamically changing over time. Research question 2: How can many different criteria and expert knowledge be combined in solving spatial decision-making problems related to the vulner-ability of critical infrastructure?

Multiple objectives and complex information variables are the common fac-tors which cause difficult decisions. In disaster management applications, deci-sions are often made by using expert intuition under time stress, which makes it impossible to guarantee that each critical component of the decision is appro-priately considered in the process. Therefore, there is a need to develop a deci-sion making method which can reduce the complexity of the decision by com-bining various variables and expert knowledge more efficiently. Research question 3: How can the uncertainty of information for spatial de-cision-making problems be better represented? How can expert knowledge be integrated into the modelling process?

Uncertainty is a critical element of many difficult decisions. The information variables which are used for decision-making are often vague due to the poor definition of class or sets within the universe. Therefore, many important deci-sions are made concerning uncertainty without knowing what will happen in the future or what the ultimate outcome will be. Often in rescue operations, deci-sions depend on the implicit knowledge of rescue personnel in the decision-making process which is difficult to quantify. Therefore, how to automatically integrate expert knowledge and the modelling uncertainty of input information into the modelling process, are important issues that need to be considered.

Research question 4: How can spatial objects´ dependencies be modelled? How can these interdependencies relationships be used in solving problems related with disaster management? Critical infrastructure such as electricity networks and telecommunication net-works can be modelled as spatial objects in GIS spatial data models. They are often dependent on each other. For instance, if we model the electricity distri-bution and telecommunication networks as spatial entities, the dependency re-lationships between the two networks can be seen from two perspectives. At-tribute dependency represents the fact that the failure of an electricity network will cause the functional failure of a telecommunications network because the

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telecommunications network needs electrical power to work. Topological de-pendency refers to the fact that the failure of the electricity distribution network may cause failures in the telecommunications network in a specific geographical area, and this is where spatial analysis should take place. Therefore, from the theoretical point of view, a good way of modelling this combinational relation-ship of spatial objects can bring advantages in analysing the vulnerability of crit-ical infrastructure for disaster management.

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2. Theoretical foundation

This section briefly introduces the theories and techniques that are used to de-velop a spatial decision support system for analysing the vulnerability of critical infrastructure. The main motivation in the choice of the theories comes from the difficulties in decisions making which are related to identifying the vulner-ability of critical infrastructure for disaster management.

Figure 1 illustrates how the key theories are used. The vulnerability of critical infrastructure can be affected by many factors such as human activities, topo-logical structure, and spatial location of the infrastructure and functional failure of the system. In the decision-making process, each factor is represented as a set of variables which can be used as evaluation criteria. Broad sources of diffi-culty in making decisions are commonly caused by the variables, which are often complex, dynamic, uncertain, and multivariate. A further complication is the existence of a causal relationship between the variables. A typical example is population information data which is used to describe human activities that could have an effect on the vulnerability of infrastructure. Population infor-mation is dynamic since people move to different places over time, therefore, dynamic modelling of population information is important in vulnerability analysis. Spatio-temporal modelling theory provides good fundamental sup-port in modelling population dynamics.

On the other hand, the vulnerability of critical infrastructure can be evaluated on the basis of several variables and difficult to combine. We address this prob-lem by using MCDM, so each variable can be used as an evaluation criterion to measure the vulnerability (performance) of a critical infrastructure element in relation to the objective of the decision. Moreover, fuzzy logic was used to solve the problem of the vagueness of the variables, since all the decisions are made under uncertainty and there is no way of knowing precisely how all the factors not under control will play out.

Many parts of a country's infrastructure, such as an electricity network or a transportation network can be modelled as graphs in a spatial data model, where the network itself is represented as lines and it’s starting, ending and in-tersection points as vertices. The vulnerability of a spatial network can simply be affected by the complexity of the network´s topology. For instance, a road which connects an island can be considered vulnerable since the island will be isolated if the road is cut off. Graph theory and centrality measures can be used to measure the centrality importance of spatial networks, i.e. a vertex is vulner-able if it is the most central node in the graph.

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Moreover, critical infrastructure are dependent on each other and the failure of one part of an infrastructure may cause the failure of another type in a par-ticular geographical area. Modelling the causal relationship of spatial objects becomes essential and we thus use an influence diagram theory to model this problem.

Figure 1 Interconnection between the vulnerability of critical infrastructure and key theories.

2.1 Spatio-temporal modelling

In Geographical Information Science (GIScience), real world phenomena are represented using a spatial data model, where each real world object is modelled as a spatial object. Spatial object refers to the object that contains a spatial do-main (Longley et al. 2005). Spatial object can be discrete such as points, lines or polygons that represents the spatial phenomena as continuous surface or layer (Longley et al. 2005). Spatial object contains several dimensions, in which include spatial, graphical, temporal and textual/numeric (Worboys, 1994). For instance, a house can be modelled as spatial object in spatial data model, it has its coordinates in the real world (spatial dimension), a polygon representation representing its cartographic form (graphical), time when it was con-structed(temporal), and attributes describing the building material or number of people living inside the building ( textual/ numeric) .

Time (temporal dimension) of the spatial object can be divided into two cate-gories in spatial data model. Database time refers to the time when transaction take place in information system. Event time refers to the real world time when events actually occur in the application domain (Worboys, 1994). Spatio-tem-poral model is used to model spatial objects ´relations with space and time, and their inter-relations in space and time. Various type of spatio-temporal models have been developed in the literature and examples include Peuquet and Duan (1995) event based spatio-temporal data model, Langran(1993) feature based

14

approach, Yuan (1994)´s three domains model, and Armstrong(1988) snapshot model.

The entity-relationship model uses the concepts of entity, attribute and rela-tionship (Worboys 1990, Chen 1976). An entity type is an abstraction of class of entities which are similar (Worboys 1990). For example, a building is an entity with address. An attribute is an element of data which associated with an entity. For instance a building has attribute type population and such a population is an example of attribute occurrence. A relationship is an association between en-tities such as lives in is relationship between entities person and building. Re-lationship may have attributes for example the time duration which gives the length of time that a person lives_in a building. Aggregation is often used in spatio-temporal modelling. Aggregation is the construct which enables types to be amalgamated into a higher order type and attributes of whose objects are a combination of the attributes of the objects of the constituent types (Worboys 1990).For instance, spatial object office building can be aggregation of many office buildings.

In object oriented system, all conceptual entities are modelled as objects and objects contain instance variables (Rumbaugh et al. 1991, Banerjee et al. 1987). Object oriented modelling has been used in various types of applications (In-dome and hutton 1992, Worboys 1992, Frihida et al. 2002). Object oriented spatio-temporal model represents the world as a set of discrete objects consist-ing of spatio-temporal atoms by incorporating a temporal dimension orthogo-nal into the 2D space (Worboys, 1992). Spatio-temporal atoms can be stacked on top of existing ones when events occur. Each spatio-temporal atom contains changes in both space and time, but no changes are recorded between them (Worboys, 1992). Therefore, this model is suitable for modelling the complex phenomena since it breaks through the limitation of relational form and directly captures the in-depth semantics of the application domain. However, this model is not able to model gradual changes in space through time since the spatio-temporal objects are discrete. This object oriented model later developed into Bitemporal model by Worboys (1994). It is also an event based model, so bitem-poral elements is the union of a finite set of Cartesian products of intervals of database and event time.

Figure 2 demonstrate an example of bitemporal elements (Worboys 1994). In this example, road segments are represented as set of objects and the infor-mation which related with planning and constructing the road is stored in the database system. In year 2000, there was information on the plan of a road abc whose construction was projected for the following year. In year 2001, there was information that roads were constructed but with different spatial configuration adefc to 2000 projection. In year 2002, a revision was made and further infor-mation was received that some parts of the road efc were not built until 2002. According Figure 2, there is no event time in which the spatial configuration ef exists in database time 2000 since the possibility of build point b has not yet arisen. In database time 2001, object ef exists from event time 2001 into the indefinite future, since a transaction has been taken place. In database type

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2002, object ef exists from event time 2002 into indefinite future since a trans-action has occurred which has revised the completion of this section of the road to event time 2002.

Figure 2 Example of bitemporal element. Modified from Worboys (1994).

Spatio-temporal modelling has been often used in various types of applica-tions, such as transportation and traffic analysis (Demšar and Virrantaus 2010, Wang and Cheng 2001), crime and incident detection (Cheng and Williams 2012, Pan et al. 2013).

2.2 Decision making

Multi-criteria decision-making (MCDM) analysis is a mathematical framework that provides tools for analysis of choice alternatives in decision planning pro-cess. It is a method for decision support where a number of different criteria are combined to meet one or several objectives and give support in decision making. Multi-attribute value theory (MAVT) is one type of MCDM methods (Hwang and Yoon 1981). Once the decision problem is identified, we need a tool to struc-turing the elements of the decision situation into logical framework and analyse theirs relationships, therefore influence diagram is needed (Dawid 2002).

2.2.1 Multiple attribute value theory

Multiple attribute value theory can be used to address problems that involve a finite and discrete set of alternative that have to be evaluated on the basis of conflicting objectives (Winterfeldt and Edwards 1986, Keeney and Raiffa 1976, Belton and Stewart 2002). Decision maker´s preference is often integrated into value function V(a).

V(a) = F(V1(a1), …Vm(am)); (1)

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Where alternative a is presented as a vector of the evaluation criteria a= (a1, …,am); aj is an estimate of this alternative against a criterion Cj, j= 1, …m; and Vj(aj) is the value score of the alternative reflecting its performance on criterion Cj via use of a value function Vj(x) (0≤vj(x)≤1). MAVT allows ranking alterna-tives based on assessing overall scores for alternatives under consideration. The simplest and most often used aggregation method in MAVT is the additive model:

(2)

Where wj >0, ∑wi= 1, wj, j=1, …m are the importance weight for each criterion assigned by decision maker. V (α) is the total value of the alternative α; vi (αi) is the simple attribute value function reflecting alternative α's performance on at-tribute i.

There are several weighting methods can be used. For instance, in simple multi-attribute rating technique (SMART), decision maker assign 10 points to the least important attribute and give points which greater to 10 to reflect the importance of the attribute relative to the least important attribute. The SWING weighting method deals with the worst and best levels of attributes. In the SWING weighting method, the decision maker assigns 100 points to the most important attribute and gives fewer points than 100 to reflect the importance of the another attribute relative to the most important attribute and the results are normalized (Winterfeldt and Edwards 1986).

2.2.2 Fuzzy multiple attribute decision making

The original multiple attribute decision making (MADM) uses crisp logic, and uncertainty of attribute is often ignored. This issue is especially important in spatial decision making application since geographical objects are often uncer-tain. To address this, we incorporate fuzzy logic and fuzzy set theory into the MADM process.

Zadeh (1965) first introduced fuzzy set theory as a mathematical theory of vagueness. If X is the universe of discourse, and its elements are denoted by x, then the fuzzy set A in X is defined as a set of ordered pairs:

XxxxA A |)(, (3)

Where )(μ xA

is called the membership function (MF) of x in A. It maps each

element of X to a membership value between 0 and 1. Figure 3 illustrate an ex-ample of fuzzy MFs and rules. For instance, the input attributes and output value were first described in terms of linguistic variables, such as low, middle, and high. These linguistic variables were represented by a fuzzy MFs. The input attribute value belongs to a certain MF when the degree of the MF μ is closer to 1. Fuzzy rules such as “If X is low and Y is high then Z is high” can be used to obtain the relationship between input and output. The if part (antecedent part) of the rule partitions the input space into a number of fuzzy MFs, and the then

17

part (consequent part) describes the behaviour of the system in these fuzzy re-gions (Zimmermann, 2001). The word and/or in the fuzzy rule are fuzzy opera-tors and used to describe a fuzzy intersection or conjunction of the input MF. It takes the minimum/maximum value of the input MFs.

Figure 3 An example of fuzzy MFs and fuzzy rules.

The typical MF types are triangular MF, trapezoidal MF and Gaussian MF. The mathematical form of a triangular fuzzy MF is shown by Equation (4) (Kauf-mann and Gupta 1985).

cx0

cxbbcxc

bxaabax

ax0

xa

,

,--

,--,

)(μ ~

(4)

A trapezoidal curve indicates the MF of a vector x, defined by the scalar pa-rameters a, b, c and d as follows (Ai et al.2013).

xd0

dxccdxd

cxb1

bxaabax

ax0

x

,

,

,

)(μ ~

(5)

The Gaussian membership function depends on two parameters c and ơ as given by

18

(6)

Where c represents the centre of the MF and ơ determines its width (Math works, 2015)

Use of fuzzy set theory in the field of MADM is introduced by Bellman and Zadeh (1970). This is defined as:

CGD (7)

Where G is the fuzzy goal, C is the fuzzy constraint, and D is the fuzzy decision

that is characterised by a membership function as follows:

))(),(min()( xxx CGD (8)

The maximising decision is then defined as follows:

))(μ),(μmin( max)(μmax xxx CGXxDXx (9)

For k fuzzy goals and m fuzzy constraints, the fuzzy decision is defined as fol-

low:

m21k21 CCCGGGD ...... (10)

And the corresponding maximising decision is:

(x))μ(x)...,μ,μ(x),...,μ(min max)(μ max Cm1C1GD kGXxx (11)

2.2.3 Influence diagram

The structure of the decision problem can be graphically described as influence diagram where level of relationships shown with nodes and arcs. A decision rep-resents a set of mutually exclusive and exhaustive actions the decision maker can take. Figure 4 shows an example of an influence diagram. It consists of three kinds of nodes and three kinds of links (Tatman and Shachter, 1990). The first type of node is called a chance node (or uncertain node) and represented as oval shaped in the diagram. It corresponds to a random variable that cannot be con-trolled by the decision-maker. Value nodes (diamond shaped) correspond to the utility function which represents a decision maker s preference. A decision node (rectangle shape) corresponds to each decision that needs to be made. In addition, conditional arcs end in uncertainty nodes and indicate that the uncer-tainty at their heads is probabilistically conditioned on all the nodes at their tails. Functional arcs end in value nodes and indicate that the utility function is a function of all the nodes at their tails. Informational arcs ending in a decision node indicate that the decision at their heads is made with the outcome of all the nodes at their tails known beforehand. Influence diagrams were originally

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developed to describe decision problems as an intuitive semantic that is easy to understand (Howard and Matheson 2005).

Figure 4 Structure of influence diagram.

2.3 Graph Theory and Centrality measures

Graph theory was first introduced by Swiss mathematician Leonhard Euler to solve seven bridges problem in year 1736 (Alexanderson, 2006). Later, it has been used in many different applications in the field of operations research and spatial problem solving for transportation, land use planning (Roberts 1978 and Taha 2007).

A graph G = G(V, E) is a pair of two disjointed finite sets V and E, where E is a subset of V×V. The elements of V are vertices, the elements of E are edges. An edge e=uv from the set E connects vertices u and v. The vertices are usually drawn as dots and edges as lines connecting each two respective vertices (Bondy and Murty 1976).

Bavelas (1948) first introduced network centrality for social networks. It de-scribes the structural importance of each vertex in the graph so vertices with higher centrality have a larger impact on other vertices. Centrality measures have often been used in graph analysis and modelling (Freeman 1977, Freeman et al. 1991, Klein 2010). Degree centrality is based on the idea that the most im-portant nodes are those with the largest number of ties to other nodes in the graph (Chakrabarti 2006). Vertex (edge) is cut vertex (edge) whose removal in-creases the number of components (West 2001).

Betweenness centrality can be defined on a vertex or an edge, and it measures how many times a vertex or an edge falls on the shortest path between other vertices in comparison with the total number of shortest paths. For the graph G: = (V, E) with n vertices, the betweenness CB (v) for the vertex v is:

,,

( )( ) stB

s t V sts t v

vC v (12)

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Where is the number of shortest paths passing across v and is the

total number of shortest paths (Barthélemy2004). Clustering coefficient used to measure the transitivity of a graph (Watts and

Strogatz 1998). Support a node i has ki neighbours and there are ni edges be-tween the neighbours. The clustering coefficient of node i is defined as

(13)

In connected graphs, a natural distance metric can be created for all pairs of

nodes, defined by the length of their shortest paths. The farness of a vertex x is defined as the sum of its distance from all other nodes, and its closeness is de-fined by Bavelas (1950) as the reciprocal of the farness, and that is:

(14)

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3. Research methods and materials

In this section, we introduce the research methods, theory and tools which were used in each publication, and explain how they can be used to solve the research questions and related decision-making problems. A summary of the research articles is illustrated in Table 2. The main research strategy is to use various computational methods to support the decision-making process in any vulner-ability analysis of critical infrastructure. In most of the articles, disaster man-agement was used as a scenario to demonstrate the usefulness of vulnerability analysis of critical infrastructure, as well as to show how to integrate expert knowledge and population information into the modelling process in order to support spatial decision-making. Table 2 Summary of the research articles.

Article Research Questions

Research Methods

Research Theories and Tools

Article 1: A spatio-temporal population model for alarming, situational picture and warning system

1 Literature survey, Research project , Experts´ knowledge

Object oriented Spatio-temporal model-ling, Software programming, Database management

Article 2: Analysis of vulnerabil-ity of road networks on the basis of graph to-pology and related at-tribute information.

2 Literature survey Case study Interview

Centrality measures, Multiple attribute value theory GIS software tools

Article 3: A fuzzy multiple- attribute decision making modelling for vulnerability analysis on the basis of popula-tion information for disaster management

1, 2,3 Questionnaire research Literature survey

Fuzzy multiple attribute deci-sion making , Fuzzy set accuracy assessment, Visual comparison of the maps GIS software tools

Article 4: Use of fuzzy decision-making approach in

2,3 Literature survey Research Project

Centrality measures, Fuzzy multiple attribute decision making,

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analysis of the vulner-ability of street net-works for disaster management.

GIS software tools

Article 5: A spatial fuzzy influ-ence diagram for mod-elling spatial objects dependencies: a case study on tree-related electricity outages

4 Literature survey Research project Case study

Spatial analysis, Fuzzy inference system, Influence diagram, GIS software tools

Article 1 provides answers to research question 1. It focuses on how to model

temporal dimensions of population information in disaster management. A spa-tio-temporal population model was developed in this research work, to estimate the number of people inside a risk area at a certain time. Figure 5 illustrates the modelling structure of a spatio-temporal population model. The model com-bines an object-oriented spatio-temporal model with the users´ knowledge, where population size is estimated on the basis of built-up environments in the real world. Spatial objects that are presented in this model, such as buildings, are not time dependent, but the knowledge (population information) that is gained from the entity relationship with the spatial object (real-world object) is time dependent. It started with an entity relationship i.e., people stay inside spa-tial objects (residential buildings) at certain times. The entity relationship here means “stay inside”. In this case, the temporal dimension of a spatial object re-fers to the time when there are people inside.

Figure 5 Illustration of method.

There are 11 spatial objects that are defined in the spatio-temporal population model, namely residential buildings, old peoples´ homes, roads, day-care cen-tres, schools, shops, restaurants and bars, industrial buildings, office buildings, shops and hospitals. For each spatio-temporal object, the population size changes individually according to time. The data used in the model is comprised of Building Information System data and national road and street database data (Digiroad) (Finnish Road Administration 2016), the topographic database (NLS 2016) and a dispersion model (Sofiev, 2006), which are used to describe the risk area. Digiroad data was used to model a road network and there is information

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about how many people pass by a road segment on average. Digiroad is a na-tionwide database which contains accurate data on the location of all roads and streets in Finland, as well as their most important physical features. Building Information System data was used to model buildings. It contains information about the floor area of the building and how many people register the building as their home address. A topographic database was used as a background map and a dispersion model was created from Finnish meteorological institute (FMI).

Four population size estimation methods were developed for the 11 spatial ob-jects and summarised in Table 3. The temporal aspect is taken into account by assigning weights to the estimated maximum or average number of people in-side each spatio-temporal object. The weights vary according to time. This spa-tio-temporal population model is implemented by using a software program-ming language with the help of GIS tools. It was used in a project called “alarm, situational picture and warning system for chemical, biological, radiological, nuclear and natural disaster incidents” to support decision-making in the evac-uation process in disaster management.

Table 3Population size estimation methods for 11 spatio-temporal objects.

S-T objects Methods Roads and residential building

Query road and building database, add together field-value: Population of road = add together “ traffic density” field value Population of residential building = add together “ total num-ber of inhabitants” field value

Office, old people´s home, day-care centres, res-taurant

Population = total floor area of the building/ floor area that one person use

Hospitals, school, hotels and industrial buildings

Use address locator to find organizations´ name, and compute population size manually

Shops Average customer for different shop size can be estimated by using statistical material.

Article 2 provides answers to research question 2. We claimed that the anal-

ysis of the vulnerability of critical infrastructure such as road networks should not only be based on the networks' topological structures, some non-topological attributes such as population information should also be taken into considera-tion. We introduced MAVT which can combine all the attributes´ values, not only topological but also non-topological, and weight them according to deci-sion makers' preferences in order to produce an overall vulnerability value for the road network. The locations which have a high overall vulnerability value

24

are considered as being critical, therefore, more effort needs to be put into the preparedness planning aspect of disaster management.

In this research work, four attributes were selected and they are: the popula-tion size and number of facilities within a 300-metre buffer-zone around the road segment; the cut edge of the road network, and the betweenness value of each road segment. Digiroad data was used for the vulnerability analysis of the road network. Digiroad data was first converted into an ASCII file where the topology information was retained in the form of the numbers of from- and to-nodes for each road segment. Geometrical or attribute information was re-moved from the data during the transformation. The graph representing the network was then transformed into a line-graph using a specially written pro-gramme. The line-graph L(G) takes the edges of G as its vertices, i.e. V(L(G)) = E(G) (Demšar et al. 2008). Betweenness centrality was computed onto the line graph by using Pajek large network analysis software (Nooy et al. 2011).

The population information data came from the Building Information System data of the city of Helsinki in Finland. It contains information about the loca-tions of buildings and the number of persons who registered a building as their home address. In this case, only the population information of residential build-ings was used to model the vulnerability of the street network and other types of buildings such as shops, office buildings etc. were ignored due to the lack of population information. We created 300-metre buffer-zones between each road-segment and selected a number of residential buildings which fell inside the buffer. After that, we calculated the total number of people who live inside selected buildings for each road-segment and attached this population infor-mation to the segment.

Table 4, illustrates an example of how to compute the overall value on the ba-sis of the above mentioned attributes for 4 road-segments. For instance, row 3 shows a value function Y=5x is assigned to the number of facilities attributed and the result is normalised in row 4. The other attributes´ value functions are calculated and normalised in the same way. The weight of the attributes is cal-culated using the SWING weighting method (Figure 6), and illustrated in the weight column.In the end, we demonstrated this method by using a case study. The first application was to perform a vulnerability analysis of the road-network for preparedness against terrorist attacks. The second application was to com-pute the vulnerability of the road-network for preparedness of rescue planning. In order to get an accurate weight for input attributes, six experts were inter-viewed. The weighting results for these two applications were presented in Ta-ble 5 and Table 6. The value function for the population size data is y=0.1x and the value function for betweenness data is y=10x. The value function for the cut edge and facility attributes is y=0.5x. After the attributes have been combined into an overall value, the number of roads that need to be protected is reduced, compared with adding the results together from every single attribute value vul-nerability analysis map.

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Table 4 Illustration of MAVT and overall value calculation methods.

Road 1

Road 2 Road3 Road4 Attribute Weight

x: Number of facilities(NF) 0 3 1 2 0.308 Value function of NF Y=5x

0 15 5 10

Normalized VF:

0 1 0.33 0.66

Cut edge VF (Normalized CE)

1 0 1 0 0.231

Betweenness VF (Normalized BN)

0 1 0.013 0.019 0.077

Population size VF (Normalized PS)

1 0.22 0 0.33 0.385

Overall value (Additive model)

0.231+0.385=0.616

0.470 0.332 0.331 -

Figure 6 Illustration of SWING weighting method.

Table 5 Weights for the corresponding attributes in the case the vulnerability analysis of a road net-work for the preparedness against a terrorist attack.

Population size Facility Cut edge Betweenness

SWING 0.42 0.33 0.17 0.08

SMART 0.47 0.35 0.11 0.05

)/()( minmaxmin vvvx

)()()()( 333222111 xvwxvwxvwxv

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Table 6 Weights for the corresponding attributes in the case the vulnerability analysis of a road net-work for preparedness for rescue in the event of a terrorist attack.

Population size Facility Cut edge Betweenness

SWING 0.22 0.04 0.3 0.43

SMART 0.27 0.05 0.3 0.36 Article 3's answers to research question 1, 2 3 are focused on how to combine

various population information variables and decision makers´ knowledge into the modelling process. On the other hand, the model should also take into con-sideration the vagueness of classification of population information. We achieve these goals by first demonstrating the role of population information in different phases of disaster management. We used fuzzy MADM modelling and inte-grated the knowledge of rescue experts into the process, to represent the com-plexity of uncertainty problems related to population information.

In this research work, we used fuzzy logic to address the issue of the vaguness of population size, so the population information is represented as a number of fuzzy membership functions instead of crisp classification boundaries. Fuzzy rules were used to combine different input variables into an output vulnerability value by using expert knowledge. For instance, the evaluation criteria of the al-ternatives considered in this fuzzy MADM model consisted of the total number of people (TP) and the total number of children (aged 6 years old or less) (TC) inside a building. We obtained expert knowledge by means of a questionnaire that asked 7 experienced rescue decision-makers to estimate various levels of vulnerability based on the values of these two input population information var-iables. This knowledge was used to create fuzzy membership functions and fuzzy rules. Figure 7 illustrates fuzzy membership functions created for these two in-put population information variables.

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Figure 7 Fuzzy MFs for input attributes.

Table 7 illustrates the fuzzy rules created in this research project. The rules were derived from the experts' answers from the questionnaire research. The final choice is based on the majority decision of the experts. In Table 7, the an-tecedent part of the fuzzy rule is the combinations of MFs of two input popula-tion information variables, and the consequent part is its corresponding vulner-ability value. The MF combinations which received the highest (HPHC) and low-est (LPLC) ranks received the extremely high (EH) and extremely low (EL) MF, respectively, in the consequent part. The MF combinations which have the ‘MPHC’ and ‘HPMC’ combination received a high (H) vulnerability value. The ‘HPLC’, ‘LPHC’, and ‘MPMC’ MF combinations received the middle (M) vulnera-bility value. The ‘LPMC’ and ‘MPLC’ membership combinations receive the low (L) vulnerability value. For instance, the fuzzy rule for the first column is: If TP is High and TC is High, then the vulnerability of the building is extremely High.

Table 7 Ranks of combinations of MFs from experts, demonstrating the antecedent and consequent part of the fuzzy rules. H: high M: middle L: low. For example, HPHC refers to high (a large) number of people and children live inside a building.

Fuzzy Rule Rank of Combination of MFs

(Most Vulnerable -> Least Vulnerable)

Antecedent HPHC MPHC HPMC HPLC LPHC MPMC LPMC MPLC LPLC

Consequent EH H H M M M L L EL

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In the end, we validated our model using visual comparison of the results to original population information map, and an innovative questionnaire method-ology combined with fuzzy set accuracy assessment. Fuzzy set accuracy assess-ment was introduced by Gopal and Woodcock (1994). Let X be a finite universe of discourse, which in this article is the set of buildings in the study area. Let ζ denote the finite set of attribute membership MF classes (or categories) as-signed to the data in X; let m be the number of categories | ζ | =m. For each, we define as the MF assigned to x. The set

Xxxx |))(χ,(Μ (15)

Defines the data. The subset of n data is used. A fuzzy set

SxxxA cc |))(μ,( (16)

is associated with each class where is the characteristic or MF of C. To implement a decision, the model uses a Boolean function σ that returns a results of 0 or 1 based on whether x belongs to the class C with respect to the matrix A. MFs are derived from linguistic values provided by the experts. The data set used for fuzzy analysis is an n by m matrix of MFs denoted as A. The row of A represents data and columns represents classes.

A linguistic scale was often used to evaluate the accuracy of the labels which are assigned to the observation object. Often the linguistic values are further converted into a numerical scale. In this article, a scale ranging from 0 to 7 based on the number of questionnaire participant. For instance, a scale of 7 means that if all seven experts thought a building should belongs to a certain attribute MF then this conclusion is absolutely right. A MAX function is defined as fol-lows:

otherwiseζC allfor )(μ)(μ if

),('

c

0xx1

CxMAX c (17)

That is, MAX(x, C) is 1 if the value of the MF for x in category C (μc(x)), is the

maximum among all the categories μc(x). Table 8 illustrates an example of using 3-by-6 matrices. This table also includes four additional columns representing sample building numbers (x = 1,…,3), numeric scales of )(μ X which are as-

signed to each buildings on the basis of the MAX function, labels assigned to the building according to experts´ opinion with the MAX function, and labels as-signed to the buildings on the basis of the model results )(χ x . For instance,

according to Table 8, 6 experts thought building 1 has a low number of people, and all the experts thought building 1 has a low number of children. According to MAX function, the experts suggested the label for building 1 is LpLc.

The accuracy of the models was finally described as the frequency of the matches and mismatches between the models’ result labels and the experts’ sug-gested labels. In order to perform the matching process, the original data were first divided into 9 categories by using labels suggested by using MAX function

29

from experts´ knowledge and each category represents one attribute’s MF com-binations and contains a set of buildings. This information was saved and called the expert-defined category. The original data were then sorted according to the vulnerability results of the fuzzy model from the highest to lowest order, and then divided into 9 categories which represent the MF combinations of the at-tributes. This is called the model-defined category. In Table 7, the experts have ranked the 9 MF combinations. Both the expert and model defined category data were arranged according to the experts’ rankings, from the highest to the lowest order. We assume the model-defined category should contain the same number of buildings as the corresponding expert-defined category. For each cat-egory, we calculate the frequency of the matching and mismatching of buildings between the expert-defined categories and the model-defined category and the results are illustrated in section 4.2.3.

Table 8 Example of using fuzzy set accuracy assessment to validate the fuzzy model´s result. n=3, m=6, AND C= {HP, MP, LP, HC, MC, LC}. The columns HP, MP, LP, HC, MC, LC form the 63 matrix A.

Building

x

Experts Evaluation cA

Questionnaire (question 1)

)(X

MAX

Function

Experts

Suggested

Labels

Models

Labels

)(x

TP TC TP TC TP TC TP TC

HP MP LP HC MC LC

1 0 1 6 0 0 7 6 7 LP LC LP HC

2 0 5 2 2 4 1 5 4 MP MC LP HC

3 1 5 1 0 1 6 5 6 MP LC MP LC

Article 4 continues the work undertaken in article 2 and 3 and is used to an-

swer research questions 2 and 3. Article 2 used crisp MAVT to combine all the attributes in order to produce an overall value vulnerability map of a road net-work, where the uncertainty of spatial information is not considered. In article 3, a fuzzy MADM model was used to compute the vulnerability of the Helsinki area on the basis of population information building register data, where the road network was ignored. In this article, population information and a be-tweenness centrality measure of the road network were used as the evaluation criteria, and a fuzzy MADM approach was used to combine both criteria to sup-port a vulnerability analysis of the road network. Population data and a be-tweenness centrality measure of the network were computed in the same way as in article 2. Two Gaussian membership functions were created for each attribute and illustrated in Figure 8 and fuzzy rules created on the basis of input MFs

30

were presented in Figure 9. For instance, fuzzy rule No. 1 means, a road which has a high population size and a high betweenness value then it follows that the output vulnerability value is high.

In this article, we use fuzzy logic instead of crisp modelling to represent the uncertainty of spatial information in order to make the model more realistic. In the end, results were compared with original population information and a be-tweenness attribute map. The results will be presented in section 4. 2.2.

Figure 8 Gaussian MFs of input attributes.

Figure 9 Illustration of fuzzy rules.

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Article 5 is used to provide answers to research question 4. Extreme weather

conditions such as storms can cause trees to fall and damage the electricity net-work. This refers to a so-called tree-related electricity outage. This scenario can be modelled as a causal relationship between hazardous trees and an electricity network since the failure of the electricity network is caused by falling trees. In this article, we model this causal relationship by using a spatial fuzzy influence diagram.

In the beginning, we developed a general structure of a spatio-fuzzy influence diagram which was used to model spatial objects´ topological relationships, to-gether with attribute dependencies (Figure 10). Using traditional influence dia-grams for comparison, fuzzy logic was used to model the uncertainty of spatial objects, and spatial analysis was added as an extension to the influence diagram to model the topological relationships of the spatial objects.

Figure 10 General structure of spatial fuzzy influence diagram.

This SFID is later modified to model tree-related outages problems where en-vironmental variables are modelled as nodes, and arcs between different varia-bles represent their dependency or influences (Figure 11). Data used in this re-search work are forest resource dataset, soil type data and the electricity net-work data along with the locations of the tree-related outages. In Figure 11, four spatial objects' chance nodes were created: the soil type node, the tree age node, the tree height node and the electricity network node. Each chance node has its particular properties. A decision node: trees and soil are within the clear width of the electricity network was created and it is conditioned on the outcome of chance nodes: soil type, tree age, and tree height and the electricity network. This indicates that we are only interested in the trees and soils which are located within the clear width of the electricity network. Spatial analysis methods; the buffer analysis was used to create a 30-metre buffer-zone around the electricity network and select the trees and soils which are located inside the buffer, to be studied.

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In the next step, we created a decision node hazard tree which indicates that the distribution for the hazard tree is conditioned on the outcome of chance nodes: soil type, tree height and tree age. The hazard tree represents the tree which has poor roots and is therefore at a higher probability of falling down. The tree is only hazardous if it is located within the clear width of the network, there-fore the decision of the hazard tree node also depends on the outcome of the decision node trees and soil are within the clear width of the electricity net-work. We answer the decision node hazard tree by reclassifying the selected soil type, the tree´s height and age, according to a risk value. We categorise Finnish soil-types into risk values based on how well they can support root growth ac-cording to Crow´s (2005) soil classification table. Trees have a high risk value if their height and age value is higher.

In the last step, the decision node risk area represents the vulnerable locations of the electricity network which contain hazard trees within the clear width of the network. In addition, tree-related outages occur more often under extreme weather conditions, therefore, the weather condition chance node was also con-sidered.

There are many uncertain factors involved in defining the risk areas' decision node. Therefore, we propose using a fuzzy approach. Three value nodes were created to translate reclassified soil types, tree age and tree height risk values into MFs. For each input variable, three triangular MFs were constructed. The risk value of input variables vary from 1 to 5, and the degree of MFs represent how likely this input risk value belongs to a corresponding MF. For instance, a tree height reclassified risk value of 1.2 is more likely to belong to a low MF in defining the risk area of an electricity network. Value node fuzzy output MFs were used to describe output MFs' (consequent part) of the fuzzy rule. In the risk areas decision node in our SFID, 27 fuzzy rules were constructed and used to represent decision makers' decisions. Some of the rules are presented in Fig-ure 11. Those MFs are used as inputs (antecedent part) of the fuzzy rules. Fuzzy Or function was used and it returns the maximum value of the sets the cell lo-cation belongs to in order to identify the places which have high membership values. The vulnerability value of an electricity network in case of tree related outages is represented as fuzzy output values.

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Figure 11 Spatial fuzzy influence diagram in modelling tree-related electricity outages.

34

4. Research results

The main results of the appended articles are summarised in this chapter. Sec-tion 4.1 answers research question 1. Section 4.1 illustrates the role of popula-tion information in disaster management. Section 4.1.1 presents a spatio-tem-poral population model which can be used to model population dynamics in or-der to support the decision-making process of disaster management.

Research question 2 is answered in section 4.2. It presents the results of using crisp MAVT to compute the vulnerability of a road network on the basis of mul-tiple input variables for two disaster management scenarios. Later this model is developed further in a fuzzy MADM model (section 4.2.2 and 4.2.3) which can be used to represent the complexity and uncertainty of the information, as well as how to integrate expert knowledge into the modelling process, in order to model the uncertainty problem related to research question 3. Section 4.3 an-swers research question 4 by presenting a spatial fuzzy influence diagram in solving tree related electricity outages. Vulnerable locations of an electricity net-work in the case of tree-related outages are pinpointed on the map.

4.1 Role of population information in disaster management.

The role of population information in disaster management is presented in ar-ticle 3. Figure 12 illustrates how to use population information to support the spatial decision-making process during difference phases of disaster manage-ment. Population information can be used for preparedness planning. For ex-ample, where to set up a rescue facility so that rescue personnel can save the most lives with the available resources and also during the response phase, where population information can help the rescue personnel to estimate the re-sources needed to transport the inhabitants from the endangered area. In the recovery phase, population information is needed for rebuilding the area, i.e. to support the decision on how many houses are needed to be rebuilt for the people who survived the disaster. Finally, population information can be used to see how human activity is related to particular disasters in the mitigation phase of disaster management.

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Figure 12 Role of population information in disaster management.

4.1.1 Spatio-temporal population model

In article 1, an object oriented spatio-temporal population model was developed to support decision-making in the response phase of disaster management. For instance, it can be used to calculate the number of people inside a risk area at a certain time after a disaster has occurred. This spatio-temporal population model was implemented by using the Java programming language. Figure 13 illustrates the user-interface of the software.

In the upper part of the window, there are lists of all the tools that help the user to interact with the background map. A chemical leakage accident in the city of Kuusankoski, Finland is selected as a case-study scenario. A dispersion model has been created by FMI to indicate the risk area and is represented as a red oval shape on the background map. The legend button is used to show the legend of the selected layer. Time was grouped into 17 categories and listed in a Set Time combo box. The time was specified as hours, so the user can easily choose the time category according to the accident time. A new window, ‘Buffer Analysis Results’, pops up after the user has clicked the ‘Analysis’ button. It shows all the 11 spatio-temporal objects. For each spatio-temporal object, a dif-ferent estimation method is used for estimating the population size (see Table 3). The user can click the ‘Show Result’ button to estimate the population size for the corresponding spatio-temporal object. For instance, Figure 13 illustrates the simulation of population size estimation methods for office buildings. After the user has clicked on the office buildings' ‘Show Result’ button, a dialog box pops up that shows the total floor area of the selected office building was 348 square metres. In the dialog box, the user can set a parameter that is used to define how many square metres one worker uses. In this case it was 23. The

36

result, which was called ‘Count People’, was calculated by using the total floor area of the selected building divided by the parameter that the user set, which gave the result as 15. After that the time dimension was given as a weight 2/3. Therefore, the final estimation of the population size was 15 times 2/3, i.e. 10. A similar user interface and method was also used for old people’s homes, day-care centres, restaurants, and bars.

For roads, hospitals, hotels, schools, industrial buildings, restaurants and shops, the estimated population size for the corresponding buildings will appear in the corresponding text field after the user clicks on each ‘Show Result’ button. The results came by querying database files and adding the corresponding at-tribute value together. The weight for different spatio-temporal objects was added after the query process. In the end, all the spatio-temporal objects analy-sis results are added together after the user clicks the ‘Total’ button. In this case, the estimated population size inside the risk area is 3,164. The ‘Report’ button is used to create a text file of analysis results. The ‘Save’ button is used to save the report. As a result, the model will produce a text file, which can easily be adapted to other systems.

This spatio-temporal population model will give support to decision-making problem I in Table 1. With this spatio-temporal population model, rescue per-sonnel can easily estimate the number of victims which are inside a risk area at particular time. This information can help rescue personnel improve rescue ef-ficiency and optimise rescue resources.

Figure 13 Spatio-temporal population model software user interface.

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4.2 Spatial decision models for vulnerability analysis of road net-work

Crisp and fuzzy MCDM models were created for modelling the vulnerability of road networks for disaster management. The results are presented in the fol-lowing sections.

4.2.1 Crisp multiple attribute value theory decision model

A crisp MAVT decision model was used to combine not only the topological but also non-topological attributes to create an overall vulnerability value for the road network.

The first application was to perform a vulnerability analysis of the road net-work for preparedness against terrorist attack, and the result is illustrated in Figure 14. Results were compared with original normalised population size, be-tweenness and cut edge attribute maps which are illustrated in Figure 15, Figure 16 and Figure 17. According to Figure 14, the map was similar to the population size distribution map, because population size was the most preferred attribute. The places which had the second highest population size value, had the highest overall value when there were important facilities located nearby. This is be-cause the important facilities attribute has the second highest weight. The northern parts of the network had middle overall value because these roads re-fer to the cut edges, and those road segments had low values in the original pop-ulation size map and high values in the cut edge map.

Figure 14 An overall value map for the first application by using SWING weighting method.

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Figure 15 Normalised population size map.

Figure 16 Normalised betweenness attribute map.

Figure 17 Normalised cut edge attribute map.

In the second application, the vulnerability map was used to help rescue op-erations after terrorists have attacked the road network. Figure 18 illustrates an overall value map. Most roads that had the highest overall values (in red) on this map, refer to the cut edge roads and the roads which had high betweenness val-ues. This is because the cut edge and betweenness value attributes were the top two preferred attributes. One red spot in the south-east part of the map refers to the places with a high population density.

39

Figure 18 An overall value map for the second application by using SMART weighting method.

4.2.2 Fuzzy multiple attribute decision making model

The results of using the fuzzy MADM model to analyse the vulnerability of the road network were shown in Figure 19. The most vulnerable roads were repre-sented in red on the vulnerability map. The most vulnerable locations were parts of the road segments in Ruoholahti, Herttoniemenranta, Vallila, and Ki-viruukki. The most vulnerable roads also included a part of Turunväylä, Kehä ring No. 1, Vihdintie, and the intersection point of roads Nos. E75 and 7.

The model results were validated against the original population information attribute and betweenness attribute maps (Figure 20 and Figure 21) in order to see if the roads’ vulnerability values matched the original input attribute infor-mation. The comparison results showed that the vulnerability map had similar patterns to the betweenness value attribute map. For instance, in the middle of the vulnerability map, the red lines which represented part of Turunväylä, Kehä ring No. 1, and their connecting roads also had a high value on the betweenness attribute map. The betweenness value map showed that Haltialantie, Fallintie, and Kuninkaantammentie had the highest betweenness value, but most of those roads received the second lowest vulnerability value because of the low popula-tion size attribute of the roads. The same idea also applied to the other major roads such as part of Kehä ring No. 3 and the E75.

On the other hand, the vulnerability map also had similar patterns to the pop-ulation attribute map. For instance, the three star-shaped red spots in the south-ern part of the vulnerability map refer to the places with a high population den-sity. For instance, the hot spot in Herttoniemenranta refered to road segments which had the highest population size and second highest betweenness value on the original input attribute maps. Herttoniemenranta was a critical location be-cause it connects the eastern part of Helsinki to the city center. The Finnish gov-ernment planned to build a new bridge over the sea in Kruunuvuori to share the heavy traffic load of this area. Länsiväylä received the lowest vulnerability value because most of the road segments have the second lowest values on both the population and betweenness attribute maps.

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Figure 19 Vulnerability map of road network.

Figure 20 Population size attribute map.

Figure 21 Betweenness attribute map.

By using crisp MAVT and fuzzy MADM modelling, the numbers of hot spots from the original variable maps were reduced to a reasonable scale, and the

41

places which have both high input values were clearly pointed out. This will help to solve decision problem III in Table 1. It illustrates the vulnerable locations of road networks in case of disaster.

4.2.3 Model the complexity and uncertainty of population information in disaster management

In article 3, a fuzzy MADM model was developed to show the vulnerable loca-tions of the Helsinki area on the basis of population information for disaster management. It can be used to model the complexity of population information, since various types of attributes of population information can be combined in the modelling process. We use fuzzy logic to address the uncertainty of popula-tion information and experts’ knowledge together with the MADM procedure that allows us to combine population information variables into a measure of vulnerability that can be used to optimise the efficiency of the long-term deci-sion-making process.

The input parameters of the model are the number of people and children in a building. The number of people in a building was used as a proxy of how densely a building is inhabited and the number of children was considered as a proxy of necessity of rescue intervention. The vulnerability of a building was therefore defined by these two variables: the higher the number of people and children inside a building, the more vulnerable the building. The exact criteria to derive the level of vulnerability were based on fuzzy logic and experts’ knowledge. Figure 22 illustrates the kernel density maps with search radii of 250, 500 and 750 metres based on results from fuzzy MADM models. Areas which had a high kernel density value in the resulting vulnerability map referred to places which had a high density of buildings and/or high output values in the model.

The Helsinki area was divided into eight rescue zones, zones were then visu-alised together to produce a model result map for the entire Helsinki area. In this way, the kernel density at a specific location is created on the basis of a cer-tain zone’s data value. In the maps with 500- and 750- meter search radii, the most vulnerable regions were regions Nos. 0, 8, 30, 44, 61, and 77 and the in-tersection part between regions 1, 2, 3, and 4, the intersection parts between regions 15 and 18, the intersection parts between regions 33, 34, and 36, and the intersection parts between regions 51 and 52.

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Figure 22 Kernel density map of population information by using fuzzy model normalised results.

Model results were first validated against the original population information kernel density maps (see Figure 23 and Figure 24). Results show that the vul-nerability maps display a similar spatial pattern as the original population in-formation map. The number of hot-spots in the vulnerability map was reduced to a reasonable number compared to the original population information map. In the second step, the model was validated by using fuzzy set accuracy assess-ment and the actual domain knowledge of rescue experts.

The results of the frequency of the matches and mismatches for the fuzzy model are summarised in Table 9. The categories column represents both the expert-defined and model-defined categories and they contain the same MF combinations and the same number of buildings. They were arranged according to the expert-ranked order. For instance, the experts thought the category HPHC was the most vulnerable category and it contains 12 buildings. If we sort the data according to the fuzzy models’ results in descending order, the top 12 most vul-nerable buildings should have the HPHC MF combination according to the ex-perts’ opinion, and they should be the same buildings as those which the experts defined as belonging to the category HPHC. According to the results shown in Table 9, the fuzzy model produced very high accuracy in the HPHC, MPMC, MPLC, and LPLC categories and low accuracy in the MPHC, HPMC, HPLC, and LPMC cate-gories. The low accuracy of the results mainly happens in the categories which contain less than 40 buildings, except for the most vulnerable category.

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Figure 23 Kernel density map of population information by using normalised population size attribute values.

Figure 24 Kernel density map of population information by using normalised number of children attribute values.

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Table 9 Validation of the fuzzy model by using fuzzy set accuracy assessment and domain knowledge of rescue expert. Hp: high number of people, MP: Middle number of people, LP: low number of peo-ple, Hc: high number of child, Mc: Middle number of child, Lc: low number of child.

The advantage of using fuzzy modelling is that the numbers of hot spots from

the original population information maps were reduced to a reasonable scale and the locations which have large numbers of people and children living in them were clearly identifiable on the fuzzy vulnerability map. The results of this study will support decision-making problem II of Table 1. The hot-spot refers to those areas where rescue intervention is most needed.

4.3 Analysis of vulnerability of electricity network in a case of tree-related outages

The vulnerability map of electricity network in a case of tree-related outages is presented in Figure 25. The vulnerability of networks refers to the degree that electricity networks suffer from tree-related outages and it is the fuzzy output MF value of the fuzzy rules in the SFID model.

A visual comparison of the predicted vulnerability value and electricity faults data were used as one validation method to see the accuracy of the model. In the second validation method used, the percentage of fault data which received a value in a different vulnerability category was calculated. The results showed that the fuzzy model produced high accuracy in some predicted vulnerability categories, for example, 54 % of fault locations received at least a high vulnera-bility value and the low vulnerability category received a rather low percentage (19%) compared to other categories.

According to Figure 25, the vulnerable locations of an electricity network were pointed out on the map in order to support electricity network maintenance and planning. This will answer the decision making problem IV in Table 1

Category Total Expert Evaluation (Max Methods)

Match Mismatch

HPHC 12 11(92%) 1(8%)

MPHC 11 3(27%) 8(72%) HPMC 21 6(29%) 15(71%) HPLC 22 0 22(100%) LPHC 0 0 0 MPMC 431 322(75%) 109(25%) LPMC 36 0 36(100%) MPLC 2779 2344(84%) 435(16%) LPLC 28676 28344(99%) 322(1%)

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Figure 25 Vulnerability map of electricity network in a case of tree-related outages.

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5. Discussion

In this dissertation, several computational methods were used to support deci-sion making which are related with vulnerability analysis of critical infrastruc-ture for case of disaster management.

5.1 Spatio-temporal population model

A spatio-temporal population model was developed to support the decision-making process in emergency and disaster situations. The model combines an object-oriented spatio-temporal model with users´ knowledge. Population size is estimated on the basis of built-up environments in the real world. Built-up environments such as buildings and roads are divided into different categories; each category is one spatio-temporal object, and population size changes ac-cording to time. The model produces reasonably accurate results since each spa-tio-temporal object is modelled separately according to its own characteristics, and experts can frequently update their knowledge to improve the accuracy. For some categories of spatial objects, such as industrial buildings, hospitals, schools and hotels, the population size information comes from the webpage of each organisation, which have high accuracy but the data collection is time con-suming.

On the other hand, there is no validation method developed in this research work to validate the model, so the actual accuracy of the model cannot be eval-uated. There are several sources of uncertainties that are involved in the model. First of all, the temporal dimension (time) was modelled as weighted to the es-timated maximum or average number of people inside each spatio-temporal ob-ject. The actual weight is difficult to set and it depends on the implicit knowledge used in the experts’ decision-making process, which is difficult to quantify. For office buildings, old people´s homes, day-care centres, restaurants and bars, the population information was estimated on the basis of the total floor-area of the building, divided by the average floor-area that one person uses. Statistical re-search on average floor-area that one person uses is not available for all the above mentioned building types and the value is based on an average estimation with a low level of accuracy. Digiroad attribute data on municipal street, private roads, as well as pedestrian and cycle routes are maintained by municipality. The responsibility for maintenance is based on the Road and Street Network Information System Act (Finnish Road Administration 2016). However, the ac-curacy of population information in Digiroad data is low.

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5.2 Multi-criteria decision model

Various types of critical infrastructure such as transportation and electricity networks can be represented as spatial networks in spatial data models. The de-cision-making problems which are associated with critical infrastructure vul-nerability can be simply affected by the complexity of a network's topology. Graph theory and sets of centrality measures were used to model the spatial network's topological importance. Often, it is not always sufficient to perform the vulnerability analysis of critical infrastructure only on the basis of topologi-cal structure, some non-topological attributes such as population information should also be considered. Therefore, multi-criteria decision analysis was used to combine various types of input variables not only topological variables, but also population information to compute an overall vulnerability map of critical infrastructure. For instance, road segments which have a higher overall value are more vulnerable than others and need more preparedness in case of a dis-aster.

Moreover, the uncertainty of geographical information always exists, and a typical example of uncertainty is the vagueness of classification of the infor-mation. For instance, it is difficult to say exactly what number of people living in a particular area constitute a high-risk area of a road network. We address this problem by introducing fuzzy concepts into the MADM modelling process. We applied this methodology to two applications. The first application is to ap-ply this method to road network vulnerability analysis. The betweenness value and population size were selected as input variables. The results showed that the vulnerability maps are similar to the vulnerability map which was computed by using the crisp MAVT model, but the number of hot spots are much less than the crisp MAVT model results. One of the reasons is that the input variables in the fuzzy MADM model are less than in the crisp MAVT, the crisp MAVT model uses four input variables and the fuzzy MADM model uses only two. Another reason arises from the fuzzy method itself, since all the input and output varia-bles are represented as degree of membership functions which cause the fuzzy MADM model to have less diversity of output variables than the crisp MAVT model.

In the second application, we apply a fuzzy MADM model to the city of Hel-sinki building register data in order to support rapid decision making in emer-gency situations. The model results were first validated by comparing them with the original population information maps. In the second step, the model was validated by using a fuzzy set accuracy assessment and actual domain knowledge of rescue experts. However, the accuracy of the fuzzy model was low for the categories which contain less than 40 buildings. The uncertainty of the results is derived from several sources. The first source is the conflicting ques-tionnaire answers as given by the experts, since fuzzy MFs were created on the basis of the range and average value of seven experts' answers to a question-naire, and the experts came from different rescue organisations and have differ-ent backgrounds. Therefore their answers may in some cases differ significantly. Moreover, the model validation process used the majority of the answers from the questionnaire research which means that the fuzzy decision rules in the

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model reflected the average procedure used in emergency response situations across all zones and employing all types of expertise.

5.3 Modelling spatial objects´ dependency

In this dissertation, a new methodology – spatial fuzzy influence dia-gram(SFID), was proposed to model spatial objects' dependencies. In the SFID, a spatial object´s topological relationship can be modelled together with the at-tribute dependency of the object, and the object´s spatial context can also be involved. This spatial extension provides the ability to answer the question; "where are the areas that are at risk"? In addition, fuzzy logic was used to solve the problem relating to the vagueness of classification. This SFID methodology is more general and easier to adapt to different applications.

A visual comparison of the predicted vulnerability value and electricity faults-data were used as one validation method to see the accuracy of the model. In the end, the percentage of fault data which received a value in a different vulnera-bility category was calculated. The results showed that the fuzzy model pro-duced high accuracy in some predicted vulnerability categories, for example, 54 % of fault locations received at least a high vulnerability value and the low vul-nerability category received a rather low percentage (19%) compared to other categories. The error source of the case study results comes from many perspec-tives. Here, we demonstrate a framework of using SFID to model tree related electricity outages. It was not our intention to produce high quality case study results in this article; which means the fuzzy rules and fuzzy MFs are not pro-duced in the real domain. This is the major error source of the results. The sec-ond error source comes from the reclassification of tree and soil data. Soil type risk reclassification was constructed by matching Finnish soil map classification with Crows´ (2005), soil classification, and the accuracy of the match is difficult to evaluate. The third error source is involved in the clear width calculation around the electricity network. The clear width calculation is not estimated based on the height of the electricity network due to a lack of electricity network height data. In the future, electricity networks' height data could be included in a clear width calculator so the results would be more realistic.

5.4 Future work

Mobile data has often been used in modelling population dynamics, as re-ported in the literature (Bengtsson et al. 2011, González et al. 2008, Deville et al. 2014). The difficulties related with mobile data arises from the privacy issue and availability. There are limitations regarding the use of mobile data under challenging environmental conditions. For example, mobile devices will not function under water or in a fire which is a real drawback when using mobile data in disaster management. In addition, most of the mobile data is large and often represented as dynamic trajectories which are difficult to analyse and in-terpret. In emergency situations, rescue personnel are working under time pres-sure and there is simply no time to conduct an analysis of such a large dataset,

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and the spatio-temporal population model should be designed so it is simple and easy to use.

Moreover, the dataset which used in a spatio-temporal population model should be available at a national level, so it can be used efficiently in the event of a disaster. In Finland, each municipal authority has the responsibility to col-lect their own Building Information System data, so in the future this model can be implemented for all the other cities in Finland. The model can be also up-dated into a web-based application so different rescue departments can auto-matically exchange population information and improve rescue efficiency. In the future, it will also be possible to improve the model by including more spa-tio-temporal objects i.e. forest and ship data, in order to make it more realistic and accurate. Various data sources, such as commuting information derived from volunteered GPS trajectories, can be used to validate the model.

The accuracy of the crisp MAVT model can be improved by analysing the weight of the attributes more carefully, i.e. developing a suitable method to col-lect expert knowledge. A sensitivity test should be included in order to see how sensitive the model is in relation to changing the attribute weights and value functions. The centrality measure of the network was computed by using the Pajek software tool and the actual shortest path between two vertices was cal-culated on the basis of the number of vertex passes, not on the actual length of the path. In order to solve this problem, a new shortest path algorithm has been programmed by using the Java programming language and used for testing the topological importance of Finnish city, Tampere's road network.

Fuzzy MADM was used to identify the vulnerable locations of the Helsinki area, based on building base register data. In the application, the uncertainty of the results comes from the conflicting answers provided by experts in the ques-tionnaire research. In the future, this problem can be solved by creating local fuzzy decision rules where only rescue personnel from that particular zone should participate in the knowledge acquisition process. The fuzzy MADM model only takes into account two population variables; the total number of in-habitants of a building and the number of children in a building. In the future, other demographic variables, such as the number of elderly people and/or peo-ple with disabilities, should also be taken into consideration. Furthermore, the level of vulnerability for disaster management should be dynamic, as has been reported in the literature (Ahola et al. 2007, Špatenková and Stein 2010), and in this research work the data on the inhabitants of the residential buildings are used and the time when inhabitants are inside the building are unknown. A spa-tio-temporal model could be developed by including more building types and modelling people´s daily migration behaviour, which could be derived from var-ious sources, i. e. GPS trajectories (Shen et al. 2013).

In order to improve the results of case studies by using SFID, it is necessary to develop a new study of how local soil types can support the growth of tree spe-cies' roots, and take into consideration all the different tree species in the local forest. All the fuzzy membership functions and fuzzy rules should be created by domain experts in order to make the model realistic. In addition, the network outage dataset contains 223 fault locations which are collected from the year

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2013 to 2015. Obviously, many vulnerable locations of the electricity network do not have fault-data available to validate. Therefore, more fault-data prior to the year 2013 should be included in order to make the validation process com-plete and accurate. A sensitivity test of the model could be also included in SFID in order to see how the result changes according to the change of expert knowledge. In the future, if the probability of the input variable is known, this SFID can be also further developed by using Bayesian network, so the probabil-ity of tree-related outages can be estimated.

In this dissertation, only two types of critical infrastructure i.e. road networks and electricity networks, were under consideration and definitely other types of critical infrastructure should be considered in the future. For instance, work has been done to develop a data driven method to analyze huge quantities of time sensitive waste water data in order to predict the vulnerability of sewerage sys-tems.

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6. Conclusion

Various types of spatio-temporal modelling techniques have been reported in the literature (Peuquet and Duan 1995, Langran 1993, Yuan 1994, and Arm-strong 1998), and object oriented spatio-temporal modelling combined with ex-pert knowledge was used to model population dynamics on the basis of built-up environments. This spatio-temporal population model is flexible, since many estimation methods are based on experts´ knowledge and experts can update the knowledge frequently, i.e. with the help of statistical analysis, in order to improve the accuracy of the results. This model can be used to estimate the number of victims inside a risk area and therefore optimise rescue efficiency and save rescue resources. In can also be used in some other applications such as the field of business. For instance, it can help a company to choose the place and time for business activities according to the area's population data.

MCDM was used to solve the decision-making problems which related to con-flicting objectives. It was used to combine different types of attribute variables related to the vulnerability analysis of critical infrastructure, into an overall vul-nerability value, in order to support decision-making for disaster management. The biggest benefit of combining all the attributes is to save resources in pre-paredness planning of disaster management. After the attributes had been com-bined into an overall value, the number of hot spots from the original input var-iable maps were reduced to a reasonable scale, and the location that needed to be protected is reduced, compared with adding the results together from every single attribute value vulnerability analysis map.

In addition to a traditional MCDM model, we extend fuzzy logic to the model-ling process to solve three types of spatial decision-making problems. Experts’ knowledge acts as an important element in many spatial decision-making prob-lems, but it is often not easy to obtain or represent. Fuzzy logic can systemati-cally and mathematically emulate human reasoning, and allows for experts’ knowledge to be incorporated into the modelling process. To achieve this, we implicitly captured this knowledge through a dynamic questionnaire and based our fuzzy model on the empirical results. Another challenge in the spatial mod-elling problem is how to validate the mathematical models against experts’ knowledge and real-world phenomena. A fuzzy set accuracy assessment ap-proach was used to validate the fuzzy models against empirical results from the questionnaire. Moreover, a spatial decision is often made under a condition of uncertainty. Fuzzy logic can be used to solve problems which are related to vagueness of classification, so input and output variables are represented as a set of membership functions instead of crisp classified values.

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An influence diagram is a graphical representation of decision-making prob-lems. It helps decision-makers to structure the decision-making problem and observe the causal relationship and interdependencies between the decision variables. In this dissertation, a traditional influence diagram was extended by using spatial analysis ability and fuzzy logic in order to model spatial object de-pendencies. This SFID was tested by using a tree-related outages case study. Results showed that it is a suitable method to model tree and electricity network dependencies in the case of tree-related outages. The vulnerable locations of an electricity network were pinpointed on the map in order to support electricity network maintenance and planning. For instance, decision-makers can priori-tise the areas for a tree trimming programme, or optimise repair resources in the case of outages which are caused by extreme weather conditions.

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