1

:

: 7698

2

:

, 2016

3

: 7698

././

4

:

:

: :

5

.

, ,

. , ,

, ,

,

.

,

, .

.

, .

, .

.

.

,

,

.

.

6

Regards

I would like to warmly thank my Professor, Petros Groumpos for his breaking ideas because he

guided me to a new path of knowledge, enthusiasm, passion, systematic research and teaching.

Also, for his valuable advice, organising guidance, his unlimited availability and the immediate

access of the results of their research. Furthermore, I thank him for the opportunity he gave me to

deal with the interesting topic of this thesis, for the encouragement he have given to me despite

my despondency and impatience. He provided me essential support throughout the preparation of

my thesis.

I would also like to pay thanks to mister Perdios for his appearance in the presentation of my thesis

as his knowledge would become crucial for further analysis and deepening of the content of my

thesis.

I also thank the doctorate Antigoni Anninou for her valuable advice and the time spent to complete

my thesis.

Finally, I would like to focus on two very important people in my life, my parents, as well as the

confidence and respect they have shown me. Without the principles and values they taught me, I

would not be capable of completing successfully my academic course. The special thanks is just

to mark the sacrifices they have made to be able to deal with the difficulties of life and become a

useful member in society.

7

2015-2016 :

. ,

Alzheimer

. ,

.

. T, .

,

,

,

.

. , ,

, ,

.

. ,

. ,

,

. ,

(FCM Toolbox)

.

,

. , Toolbox

.

.

, -

.

8

Summary

The development of this thesis was carried out during the academic year 2015-2016 and consists

of the following chapters:

The first chapter is an introduction to Automatic Control and applications that it finds in the

scientific and social sector as well as becoming a reference in the basic concepts of Fuzzy Control

and the utility that it has to address complex systems. Finally, the aim of this thesis is presented.

The second chapter discusses the illness of Alzheimers disease, describing the causes and

consequences that surround those suffering from the disease. Furthermore, reference is made to

the existence of specific genetic disease as well as epidemiology and finally multiple ways are

given to deal with it.

The third chapter is a review of basic definitions of Fuzzy Logic and membership functions. It

also defines the basic properties of Fuzzy Sets, operations and transactions properties with Fuzzy

Sets, linguistic variables and modifiers, Fuzzy Logic operators and finally describes the structure

of a Fuzzy Controller.

The fourth chapter describes the Fuzzy Cognitive Maps and mathematical models that govern.

It also analyses the development process and the creation of FCMs and corresponding methods

are proposed. Furthermore, reference is made to calculate the correlation degree, the

determination of weights using linguistic rules and linguistic variables and defuzzyfication

method. Finally, we describe the toolbox of FCM and it is given a typical example for the

complete assimilation.

The fifth chapter reviews the Decision Support Systems, competing fuzzy cognitive networks

and Intelligent Decision Support Systems. Finally, it is being described the finding stage of

Alzheimers disease using the toolbox of Fuzzy Cognitive Maps.

The sixth chapter analyses the finding stage system of the disease using more experts and its

effects on the final result.

In the seventh chapter, observations and conclusions are generated by the operation of the

system that we illustrated in the previous chapters.

9

1 ........................................................................................................11

2 Alzheimer...........................................................................................17

2.1 Alzheimer17 2.2 .19 2.3 ...20 2.4 .22 2.5 24 2.6 ..25

3 .............................................................................................29

3.1 .29

3.2 30

3.2.1 MATLAB...32

3.3 42

3.3.1 .43

3.3.2 ...45

3.4 45

3.5 .48

3.6 ..48

3.7 .51

4 ............................................................................55

4.1 ...55 4.2 .56 4.3 ...57 4.3.1 .57 4.3.2 58 4.3.3 ...59 4.4 .60 4.5 ..62 4.5.1 .63 4.5.2 ...66 4.5.3 ..68 4.6 .70 4.7 FCM73

5 ............................................................78

5.1 ..78

5.2 (CFCM) .79 5.3 (Intelligent Decision Support Systems - IDSS)..80

10

5.4 ..81

6 ......................................................................................94

6.1 ...94

6.2 ...96

6.3 101

7...110

7.1 -.110 7.2 ..111

...112

11

1

.

, , .. ,

.

-

. ,

- . , (

) (multi-variable)

- .

.

-

.

[1].

- .

.

, ,

....11

12

.

1.1

-

.

.

, -. ,

.

. , ,

- ,

.

:

13

1.2

,

, .

:

:

.

: H .

:

.

, ,

( ).

14

: ,

,

. , ,

.

:

,

. ,

.

.

: ,

.

,

.

:

,

.

,

. :

( fuzzy expert system)

Boole

.

:

if a is low and b is high then c is medium.

a b c .

15

a b c . "low"

a, "high"

b "medium"

c.

"" ,

"" ()

.

.

( knowledgebase).

:

(fuzzification)

,

.

( Fuzzy Inference Engine)

.

. MIN- (

Mamdani ) -PRODUCT ( Larsen)

.

(composition)

,

.

() o

(defuzzification)

(crisp number).

Clinical Decision Support System (CDSS)

(CDSS)

,

.

(active knowledge Systems), 2

16

.

(DSS) (knowledge management)

[2].

.

CDSS

. ,

. ,

CDSS

. , CDSS

CDSS

. , CDSS (suggestions)

.

17

2

Alzheimer

2.1 Alzheimer

Alzheimer [3],[4].

. , ,

1906

.

2.1: [19]

2.1 Alzheimer..17

2.2 19

2.3 ..20

2.4 22

2.5 ...24

2.6 .25

18

65

50 .

Alzheimer ,

.

.

, , .

.

Alzheimer

.

, ,

, , , . ,

.

. , Rowan

University School of Osteopathic Medicine

Alzheimer [5]. ,

Robert Nagele

,

.

7

14 .

,

.

[6].

18 30

. ,

.

, .

,

500

. ,

Alzheimer ,

.

19

2.2

Reisberg

.

[9],[60]:

,

.

,

.

.

, ,

.

.

. ,

,

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.

,

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20

.

.

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. 30%

(Delusional

Misidentification Syndrome-DMS),

.

,

.

.

,

. ,

. ,

,

, Alzheimer.

2.3

Alzheimer [7]:

: .

.

: () Alzheimer.

39 42

APP (Amyloid Precursor Protein)

.

(APP)

21 Down

Alzheimer 40-50 .

21

, APO-E4,

Alzheimer.

Alzheimer APP.

, ,

,

, .

: .

Alzheimer.

2.2:

[19]

22

2.4

Alzheimer ,

.

65.

Alzheimer

19 (apoE). (apoE)

. 3

e2 ,e3,e4 3

2,3,4.

6 e2/e2,e2/e3,e2/e4,e3/e3,e3/e4,e4/e4.

e3/e3 .

[8]. , 4

apoE -

40% . , 2%

apoE4 2

, 60% apoE3

85 apoE2

16,66%.

% APO-

E

APOE4

APOE3

APOE4

APOE2

23

12 -2- 30% .

tau .

Alzheimer

24

2.5

.

.

20% 40% 85 .

,

. ,

.

1000

65-69 3

70-74 6

75-79 9

80-84 23

85-89 40

90 69

2.1

65 (

25

2.3 1000

, 70-74, 1000

6, 75-79 9

1000 , 80-84 23

1000 ( 70-80 ). ,

,

2006 0.4%

2050 .

2.6

,

.

.

.

:

0

10

20

30

40

50

60

70

80

65-69 70-74 75-79 80-84 85-89 90

1000

1

26

.

, ,

.

. ,

,

[10].

,

.

, ,

[11].

, ,

.

Alzheimer

[12]. Alzheimer

,

Alzheimer

.

. , ,

. , 65%

-

.

Alzheimer.

27

,

68 %

Alzheimer

.

C , - , . ,

, C E

. ,

.

[14].

40%

6 .

(Memandine)

--D-

(NMDA) [15].

.

50% .

-

. ,

[17].

28

.

[13],[16].

-

21 . ,

.

[17].

29

3

3.1

(degrees of membership) [21]. (fuzziness)

( )

- (imprecise) ( ) .

: O . ,

. ,

.

. ,

.

1.70 .

,

.

,

,

3.1 .29

3.2 30

3.2.1 MATLAB......32

3.3 ...42

3.3.1 43

3.3.2 ......45

3.4 ...45

3.5 48

3.6 .48

3.7 .51

30

.

,

.

( universe of discourse) .

Boole () :

()

1

A

3.1 Boole ()

() =

() =

3.2

H

[0,1] [20].

31

={x}. (fuzzy set)

(membership function) :

= {()/} {()

} (. )

. () (

() ) x

(degree of membership) (degree of truth) [22].

(): [, ]

32

() = {

(, )

}

3.2.1 MATLAB

MATLAB. ,

[25]:

x

a,b c [26]:

(; , , ) =

{

(

,

,

,

)

}

(. )

: (; , , ) = ( (

,

) , ) (. )

a c "" b

.

x=0:0.1:10; 0 10

y=trimf(x, [2, 5, 8]); y=f(x)

"trimf" .

Plot(x, y) y=f(x)

grid on

33

3.2 Matlab

H x

a, b, c d

[27]:

(; , , , ) = {

,

,

,

,

} (. )

:

(; , , , ) = ( (

, ,

, )) (. )

x=0:0.1:10; 0 10

y=trapmf(x, [2, 4, 6, 8]); y=f(x)

"trapmf" .

Plot(x, y) y=f(x)

grid on

34

3.3 Matlab

c [28]:

(; , ) = ()

(. )

o

c [sigc].

x=0:0.1:10; 0 10

y=gaussmf(x, [2, 5, 7]); y=f(x)

"gaussmf" .

Plot(x, y) y=f(x)

grid on

35

3.4

Matlab

H a, b

c [29]:

(; , , ) =

+ |

| (. )

x=0:0.1:10; 0 10

y=gbellmf(x, [2, 5, 7]); y=f(x) -

"gbellmf" .

Plot(x, y) y=f(x)

grid on

36

3.5 Matlab

x

a c [30]:

(, , ) =

+ () (. )

x=0:0.1:10; 0 10

y=sigmf(x, [2, 5, 7]); y=f(x)

"sigmf" .

Plot(x, y) y=f(x)

grid on

37

3.6 Matlab

H (dsigmf)

a1, c1, a2 c2

. [31]:

(; , ) (; , ) =

+ ()

+ () (. )

x=0:0.1:10; 0 10

y=dsigmf(x, [2, 4, 6, 8]); y=f(x)

"dsigmf" .

Plot(x, y) y=f(x)

grid on

38

3.7

Matlab

H psigmf a1, c1, a2

c2

[32]:

(; , ) (; , )

= (

+ ()) (

+ ()) (. )

x=0:0.1:10; 0 10

y=psigmf(x, [0, 1, 2, 3, 4]); y=f(x)

"psigmf" .

Plot(x, y) y=f(x)

grid on

39

3.8

Matlab

zmf Z-.

a b

[33]:

(; , ) =

{

(

)

, +

(

)

, +

, , }

(. )

x=0:0.1:10; 0 10

y=zmf(x, [3, 6, 8]); y=f(x)

"zmf" .

Plot(x, y) y=f(x)

grid on

40

3.9 Matlab

smf S-.

a b

[34]:

(; , ) =

{

(

)

, +

(

)

, +

, , }

(. )

x=0:0.1:10; 0 10

y=smf(x, [1, 3, 5]); y=f(x)

s "smf" .

Plot(x, y) y=f(x)

grid on

41

3.10 S Matlab

pimf -

. H

x. a d ""

b c "" .

smf zmf [35]:

42

x=0:0.1:10; 0 10

y=pimf(x, [3, 6, 8]); y=f(x)

smf zmf "pimf" .

Plot(x, y) y=f(x)

grid on

3.11 Matlab

3.3

To

x U () > 0 :

() = { , () > 0} (. )

()

U:

() = () (. )

43

a-cut

x a, :

= { , () < 1} (. )

3.3.1

(fuzzy set) (null)

, [24]:

= () = (. )

(compliment) :

= () (. )

(subset)

X,

:

() () (. )

H (intersection)

, :

() = ()() = {(), ()} (. )

44

(union) X

, :

() = ()() = {(), ()} (. )

45

(product) A X :

() = () () (. )

3.3.2

:

, ,

,

:

= (. )

:

,

, :

( ) = ( ) (. )

( ) = ( ) (. )

:

, :

( ) = ( ) ( ) (. )

( ) = ( ) ( ) (. )

3.4

(linguistic variables)

[23].

.

, , , .

46

(fuzzy logic).

:

(input 1) ,

(range) [0 - 45] high, medium low.

, [0 45]

, low={0 7.5 15 } medium={15

22.5 30} high={3037.545},

.

(trimf) .

3.12 T low

Fuzzy Toolbox Matlab

47

3.13 T medium

Fuzzy Toolbox Matlab

3.14 T high

Fuzzy Toolbox Matlab

48

3.5

(linguistic hedges)

.

,

.

() = (),

() = ()/. ,

.

x

.

3.6

min max [36]:

= (,) =

> (. )

= (,) =

< (. )

AND () OR():

AND :

49

0 0 0

0 1 0

1 0 0

1 1 1

OR :

0 0 0

0 1 1

1 0 1

1 1 1

min max

:

= = {(,)} , (. )

50

= = {(,)} , (. )

:

= = (), (. )

= = () , (. )

51

3.7

3.15

-

52

[37]:

H (knowledgebase)

(if-then rules) .

(fuzzy sets)

.

(fuzzifier)

.

(inference engine)

.

O (defuzzifier)

(crisp numbers) .

,

:

1. O

. ,

, :

: () = ()

= ()

: () = ()

= ()

:() = ()

= ()

53

2. ,

, = =

.

.

3. , ,

.

:

, Boole

:

= ( )( ) (. )

(, ) = ( ())() (. )

, Lukasiewicz :

(, ) = ( () + ()) (. )

Zadeh min max

:

= ( )( ) (. )

(, ) = (()())( ()) (. )

, Mamdani

Zadeh min :

54

= (. )

(, ) = ()() = ((), ()) (. )

, Larsen

:

= (. )

(, ) = () () (. )

4. , - . -

centroid ()

:

= ()

()

(. )

55

4

4.1

(decision makers)

[38].

,

.

.

,

,

(natural language

arguments) . (Fuzzy Cognitive Maps-

FCM)

. , ,

.

4.1 .55

4.2 ..56

4.3 57

4.3.1 ...57

4.3.2 ..58

4.3.3 59

4.4 ..60

4.5 ...62

4.5.1 ...63

4.5.2 ..66

4.5.3 68

4.6 ...70

4.7 FCM.73

56

(causal relations) (causal result) - (concepts)

[39],[41]. ,

Zadeh 30

(linguistic nature).

( )

W ( ).

4.2

(FCM), Kosko,

(neural networks) (fuzzy logic)

- (concepts)

[39].

(nodes)

-.

- .

(systematic causal

propagation) (forward and

backward chaining) (base knowledge)

(FCM) [40].

4.1: (basic structure of FCM) [42]

57

- W.

- [0,1] [-1,1]

[-1,1]. H

.

[41]. > 0 (causal increase)

- < 0 (causal

decrease)- (opposite effect)

- = [41]. ,

[-1,1]

[-1,1] -

.

.

what-if . ,

- .

,

.

, (equilibrium),

(single state)

(finite cycle of states) [39].

4.3

4.3.1

. ,

- -

.

-. ,

- ,

,

:

= (

=

) (1)

58

t,

t-1,

f

(sigmoid function) :

=

+ (2)

, (

)

[0,1] [-1,1]

-. ,

(1).

-.

= [],

, o

, . ,

t

[43]:

= ( 1) (3)

4.3.2 I

. ,

.

,

:

= (

+

=

) (4)

59

t,

-

t-1, -

- - f

(threshold function).

-

. : < ,

(5)

:

= [1((1) + 2

1)] (6)

, (6)

t,

-.

.

-.

, ,

1, , 0,

. ,

[43].

4.3.3 I

- .

,

(4):

= [

+

=

] (7)

t,

-

t-1, - ,

60

- - ,

-

f (threshold function).

:

= (1) (8)

- . (2)

, .

.

, -

- .

4.2:

[43].

4.4

,

osko, [44]:

-

61

(causal relationships) -

(strength)

, , -

, .

-

.

, - (cause-effect)

- ,

, .

- ,

(hidden) (indirect) -

.

- -.

-

-.

, (

) - .

-.

Kosko,

[-1,1].

.

: promoting (

) inhibiting ( ). ,

. ,

.

(linguistic term)

. :

62

, , ,

0.25,

0.5, 0.75,

1.0

.

4.5

(FCM)

.

.

.

.

-

. ,

-. ,

-

(events), (actions), (goals) (values)

. ,

-

- .

( ) -

. ,

[44]:

63

4.5.1

-

-. ,

,

-. ,

.

/

.

[44]:

= (

1

) ()

,

[-1,1].

.

-

.

, :

= (

1

) ()

,

.

,

. ,

""

.

64

.

. ,

,

. ,

.

' , .

,

- .

,

.

, ""

.

:

Step1: , (credibility weight)

1, = .

Step2: - , = .

Step3: , -

.

Step4:

,

(THEN)

, (ELSE)

""

: = .

Step5: ,

:

=

( =1 )

()

65

Step6: (IF) |

| 1 (THEN)

, =

.

step7: (IF) ( ),

, (ELSE)

.

END: .

,

:

.

:

= [. , . , . , . , . , . ]

, =

. = . = = . . ,

: = .

= . (

1) . ,

,

: =

( =1 )

=

[0.6+0.64+0.75+0.66+0.25]

5=

2.9

5= .

|

| ,

0.25

.

. , :

=

( =1 )

=

[0.6+0.64+0.75+0.66]

4=

2.65

4= .

.

.

66

4.5.2

,

.

(linguistic variables) .

.

,

- . ,

-

IF-ELSE

-

. .

(influence)

" (strong influence)" " (medium

influence)" [46].

-

U=[-1,1] (influence) [47]:

() = { , ,

, , , , ,

, }

, (semantic rule)

(fuzzy sets)

(membership function) [48]:

M(negatively very strong)= -75%

M(negatively strong)= -75%

67

(negatively medium)= -50%

(negatively weak)= -25%

M(zero)= 0%

M(positively weak)= 25%

M(positively medium)= 50%

M(positively strong)= 75%

M(positively very strong)= 75%

4.3:

68

Matlab 9

[-1,1]. ""

-.

-.

,

- .

min/max

(linguistic weight)

, (numerical

value) [-1,1]. ,

(defuzzifier),

(crisp weight).

- [44].

4.5.3

[41].

-,

IF-THEN .

IF-THEN -

. ,,C

[48]:

(IF) - , (THEN)

- . , -

C.

. O

-. ,

- . ,

.

.

.

69

4

-.

:

:

(IF) (small change) , (THEN)

(large change) .

:

(positively

very high).

:

(IF) (small change) - ,

(THEN) (large change) .

:

(positively high).

:

(IF) (very small change) -

, (THEN) (very large change)

.

:

(positively very much high).

:

(IF) (small change) - ,

(THEN) (very large change) .

:

(positively

much high).

,

,

(crisp

number).

70

4.6

(Center of Area),

. ,

[49]:

= ()

()

()

CoA , x ,

.

4.4: H

(Center of Sums),

. O

[49]:

=11 + 22 ++

1 + 2 ++ ()

71

n

n.

4.5: H

(Center of Maximum),

.

.

[49]:

=11 + 22 ++

1 + 2 ++ ()

n

72

4.6: : H

(Mean of Maximum),

. ,

.

[49].

4.7: H

73

4.7 FCM

FCM

Matlab. A

(Fuzzy Cognitive Maps tool),

[45].

4.8:

"File" " Set FCM Model",

-

, -

. "Results"

-.

, "Results" .

. "Run" .

"Set FCM Model's Parameters". -

.

74

-

. ,

-. ,

- ("Initial Values of Concepts")

- ("Weights Between Concepts")

.

"Concepts". ,

-

"Constant" "Variable".

[64]:

: -.

4.9: -

75

: "Finish"

-.

4.10: FCM -

, .

: "Initial Concept Values",

. ,

=

-.

76

: - "Starting Concept Values"

"variable".

4.11: -

77

: -.

: "Run", -.

4.12: -

78

5

5.1

(FCM)

,

.

-

. (MDSS)

[57].

,

, , .

(medical experts) ,

( ). ,

,

, , .

, , ,

[50].

(DSS)

5.1 78

5.2 (CFCM)

...79

5.3 (Intelligent Decision Support Systems-

IDSS)80

5.4 ...81

79

[51],[52]. H

(FCM),

,

,

[57] .

.

. , ,

[53].

5.2 (CFCM)

, (Competitive

Fuzzy Cognitive Maps -CFCM) -: -

(diagnosis-concept) - (factor-concept).

, 5.1

. -

-

.

,

80

5.1 (CFCM) -

-

-

.

-

-

.

,

.

""

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[54].

81

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.

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[59]:

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,

. , (Strong) (Very

Strong).

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. ,

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( Memory)

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83

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84

- VS M W VS S VS

W - S W S S M

S S - VW VS M S

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S VS - W S M S

VS S S - W VS VS

W VS VS VW - S M

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86

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0 0.875 0.50 0.2083 0.79 0.75 0.79

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88

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6

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6.2 96

6.3 101

95

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M VW - VW VW - VW

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97

0 0.8125 0.50 0.1875 0.8125 0.775 0.8125

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98

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6.5 1-7

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103

6.7: To

(experts).

104

:

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105

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112

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