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Statistical reasoning is a method of reasoning in the context of uncertainty and incomplete knowledge. The advancements above in the fields of information and uncertainty have naturally influenced Statistical Science. To define the overall meaning of this endeavor, we need a broad framework that can accommodate both classic statistical information and uncertainty concepts as well as new ones developed from the fuzzy approach in its broadest sense. Read More with Us: https://bit.ly/37K8sN0 Why Statswork? Plagiarism Free | Unlimited Support | Prompt Turnaround Times | Subject Matter Expertise | Experienced Bio-statisticians & Statisticians | Statistics across Methodologies | Wide Range of Tools & Technologies Supports | Tutoring Services | 24/7 Email Support | Recommended by Universities Contact Us: Website: www.statswork.com Email: [email protected] #UnitedKingdom: +44 1618184707 #India: +91 4446313550 WhatsApp: +91 8754467066
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Statistical AnalysisUsing the FuzzyApproach
An Academic presentation by Dr. Nancy Agnes, Head, Technical Operations, Statswork Group www.statswork.comEmail: [email protected]
Introduction
Contributions of Fuzzy thinking to Statistics
Applications
Outline
TODAY'S DISCUSSION
At this stage of the Information Society, one of themost pressing issues is how to regulate the cognitiveprocess while considering its inherent qualities ofuncertainty, such as imprecision and vagueness.
This has theoretical and practical consequences infields like technology, economics, and biomedicine.
Real-life events are, in fact, the primary source ofinspiration for this type of management to beconsidered.
INTRODUCTION
Contd...
Information and uncertainty are two concepts that are strongly connectedfrom a theoretical standpoint.
A lack of information causes uncertainty.
On the other hand, information may be viewed as a means of reducinguncertainty, but this is only one potential, albeit significant, perspective onthe idea.
As a result, each conceptual expansion in the realm of information isaccompanied by the requirement to manage new forms of uncertainty.
Contd...
The theory of uncertainty has significantly expanded itsconceptual breadth and methodological tools due tothe combined influence of two developments inmathematical thinking during the previous severaldecades.
On the one hand, applying the classical theory of additivemeasures (such as probability measures) to monotonenon-additive measures (e.g. possibility measures, belieffunctions, interval-valued probabilities).
The application of classical set theory to the study offuzzy sets in both standard and nonstandard forms, onthe other hand.
Contd...
Statistical reasoning is a method of reasoning in the context of uncertainty andincomplete knowledge.
The advancements above in the fields of information and uncertainty havenaturally influenced Statistical Science.
The widespread use of the basic theory of fuzzy sets in logic, mathematics, andengineering has supplied statistical methods with exciting ideas and new tools.
A constant stream of contributions has expanded statistical reasoning toincorporate fuzzy data and fuzzy uncertainty since the late 1960s.
Contd...
However, these advancements have occurred somewhathaphazardly, with contributions from various scientificcommunities and stimuli ranging from minor to majorissues (from control systems to medical diagnosis, frommarketing to environmental studies).
In light of these contributions, there is a strong desire tosystematise statistical reasoning, and this SpecialIssue is intended to be a step forward in that direction.
To define the overall meaning of this endeavour, weneed a broad framework that can accommodate bothclassic statistical information and uncertainty concepts aswell as new ones developed from the fuzzy approach inits broadest sense.
CONTRIBUTIONS OF FUZZY THINKING TO STATISTICS
The most fundamental concept in Fuzzy Sets Theoryis a fuzzy set of a given referential set (universe ofdiscourse) T, which is defined by a mapping Ấ.
Consider the case when the observed statistical datais imprecise, loosely defined, or refers to languagelabels for ambiguous notions (such as good, large,and so on).
FUZZY SETS AND NUMBERS
FUZZY RANDOM VARIABLES
Contd...
A suitable approach to dealing with such data is to "fuzzify" it by creatingappropriate "fuzzy-valued variables" that may convey theimprecision/vagueness connected with each observation.
For the sake of example, we will refer to the univariate situation in the followingsections.
The advances in this example, however, may be appropriately extended to themultivariate scenario.
A measurability requirement should be given to formally define the randomprocess leading to a fuzzy-valued random variable inside the probabilistic context.
Contd...
This condition has been built up so that theformalisation guarantees that the concepts of randomvariable and random set are extended.
Another significant contribution of "fuzzy thinking" tostatistical analysis is the way statistical models arecreated.
The focus of imprecision in this scenario is ontheoretical informational components, such as theparameters or other model characteristics.
In this context, fuzzy clustering and fuzzy regressionanalysis are two well-known examples.
FUZZY STATISTICAL MODELS
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Contd...
The so-called "Fuzzy Inference Systems" areanother source of statistical analysis inspiration in therealm of "fuzzy thinking."
A Fuzzy Inference System (FIS) is a logical frameworkbased on "if... then" rules, with fuzzified premisesand effects.
This offers the reasoning methods some flexibility,allowing us to derive meaningful assertions fromambiguous or imprecise premises.
FUZZY "IF–THEN" RULES IN STATISTICAL ANALYSIS
The use of fuzzy statistical approaches in diversesubstantive areas is the last area of focus.
The application articles in this issue are focused onthe technological and economic sectors.
Although real-life challenges inspire eachcontribution, the methodological elements arehighlighted so that the proposed models andanalytical techniques may be productively applied tosimilar real-life circumstances.
APPLICATIONS
Contd...
