. , , ,

,,,

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1.

2.

2.1

2.2

2.2.1

2.2.2

2.2.3

2.2.4

2.2.5

2.2.6

2.2.7

2.2.8

2.2.3

3. -

4.

5.


, . .

60- . . " ", , , " - ". , , , . , . "Fuzzy Sets", 1965 "Information and Control", . - "fuzzy logic" (fuzzy - , , ).

, . , " ". , . "" . , "" .

.

, - , . , - - .

, ( ) , . .

80- . . 90- 40 , (30 - ). LIFE (Laboratory for International Fuzzy Engineering), 5- , 19 - . , . , , .

. , , , .. .

.


1.

:

1)   ;

2)   ;

3)   ;

4)   ;

5)   ;

6)   ;

7)   ;

8)   .

1.

:

;

.

:

1.   :

, B A.

2.   :

, A B.

3.   : .

4.   : .

5.   : .

6.   :

7.   : ,

.

8.   : .

2.

:

;

.

:

1.   :

, B A.

2.   :

, A B.

3.   :

.

4.   :


.

5.   :

.

6.  

7. :

,

.

7.   :

.


2.

2.1

( , , , ) , 1965 . "Fuzzy Sets" ( ) Information and Control [1]. . , , ( ) [0,1], 0 1.

A

,

X , ( ), A.

M. M , M . , , .

2.2

A B - E.


2.2.1

, A B,

.

: A B.

"", A B, , B A.

2.2.2

A B ,

.

: A = B.

2.2.3

A B , A B:

.

2.2.4

- , , , :


2.2.5

:

.

2.2.6

A B :

.

2.2.7

A :

.

2.2.8

A B :

.

2.3

. , mA(x), E. E , . .

A 5 8 B 4, 1 2.

1. A 2. B

5 AND 8 4 ( ).

3.

5 OR 8 4 ( ).


4.

. - A.

5.

A , A. .

6.


3. -

- 7 14.

:

X1 ;

X2 ;

X .

7 CONTENT ()

8 EQUAL_ ()


9 CROSSING ()

10 UNION ()

11 SUBTR ()

12 MULT ()


13 ADDITION ()

14 DIZ_SUMM ( )


4.

; mA(x) < mB(x)

; mA(X) = mB(X)

; min( mA(x), mB(x))

; max(mA(x), m B(x))

; - B = : mA-B(x) = mA (x) = min( mA(x), 1 - m B(x))

; mA(x)* m B(x)

; A^ = 1-mA(X)

; B = ( - B)(B - ) = ( ) ( B) :

;mA-B(x) = max{[min{m A(x), 1 - mB(x)}];[min{1 - mA(x), mB(x)}] }

;

; A B - 0

(DEFUN CONTENT (X1 X2)

(COND

((NULL X1) 0)

((ATOM X1) (IF (> X1 X2) 1 0))

(T (+ (CONTENT (CAR X1) (CAR X2)) (CONTENT (CDR X1) (CDR X2))))

)

)

;

; A B - 0

(DEFUN EQUAL_ (X1 X2)

(COND

((NULL X1) 0)

((ATOM X1) (IF (EQUAL X1 X2) 0 1))

(T (+ (EQUAL_ (CAR X1) (CAR X2)) (EQUAL_ (CDR X1) (CDR X2))))

)

)

;

(DEFUN CROSSING (X1 X2)

(MIN X1 X2)

)

;

(DEFUN UNION (X1 X2)

(MAX X1 X2)

)

;

(DEFUN SUBTR (X1 X2)

(MIN X1 (- 1 X2))

)

;

(DEFUN MULT (X1 X2)

(* X1 X2)

)

;

(DEFUN ADDITION (X)

(- 1 X)

)

;

(DEFUN DIZ_SUMM (X1 X2)

(MAX (MIN X1 (- 1 X2)) (MIN (- 1 X1) X2))

)

;

;

;----------------------------------------------

;

(SETQ INPUT (OPEN " D:\MULTITUDE.TXT" :DIRECTION :INPUT))

(SETQ A (READ INPUT))

(SETQ B (READ INPUT))

(CLOSE INPUT)

;

(SETQ CONTENT_AB (IF (= (CONTENT A B)) "Mnowestvo A soderzitsya v mnowestve B" "Mnowestvo A NE soderzitsya v mnowestve B"))

;

(SETQ EQUAL_AB (IF (= (EQUAL_ A B) 0) "Mnowestvo A ravno B" "Mnowestvo A NE ravno B"))

;

(SETQ CROSS_AB (MAPCAR 'CROSSING A B))

;

(SETQ UNION_AB (MAPCAR 'UNION A B))

;

(SETQ MULT_AB (MAPCAR 'MULT A B))

;

(SETQ SUBTR_AB (MAPCAR 'SUBTR A B))

;

(SETQ A_ (MAPCAR 'ADDITION A))

(SETQ B_ (MAPCAR 'ADDITION B))

;

(SETQ DIZ_SUMM_AB (MAPCAR 'DIZ_SUMM A B))

;

(SETQ OUTPUT (OPEN "D:\RESULT_OPERATIONS.TXT" :DIRECTION :OUTPUT))

(PRINT (LIST 'A A) OUTPUT)

(PRINT (LIST 'B B) OUTPUT)

(PRINT 'OPERATIONS OUTPUT)

(PRINT '------------------------- OUTPUT)

(PRINT (LIST 'CONTENT_AB CONTENT_AB) OUTPUT)

(PRINT (LIST 'EQUAL_AB EQUAL_AB) OUTPUT)

(PRINT (LIST 'CROSS_AB CROSS_AB) OUTPUT)

(PRINT (LIST 'UNION_AB UNION_AB) OUTPUT)

(PRINT (LIST 'MULT_AB MULT_AB) OUTPUT)

(PRINT (LIST 'SUBTR_AB SUBTR_AB) OUTPUT)

(PRINT (LIST 'A_ A_) OUTPUT)

(PRINT (LIST 'B_ B_) OUTPUT)

(PRINT (LIST 'DIZ_SUMM_AB DIZ_SUMM_AB) OUTPUT)

(TERPRI OUTPUT)

(CLOSE OUTPUT)

;


5.

1.

15

16

2.

17


18

3.

19

20


, , , (), , . , - - .

. .


1.         , .. [] / .., ... .: , 2007. 708 .

2.         . [ ] / . .: , 1976. . 166.

3.         . [] / .. .: , 1982. . 432.

4.         , .. . [] / .. , .. , .. . .: , 2001. C. 224.

5.    [ ] : http://ru.wikipedia.org/wiki/_

6.         , .. [] / .., .., ... : , 2002. 160 .

7.         , .. Lisp. [ ] / .., .. . .: , 2003. . 79.

8.         . [] / ., .. .: , 1990. 460 .

1. 2. 2.1 2.2 2.2.1 2.2.2 2.2.3

 

 

 

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. , :