7.1?? (1)

1
???

• ???????

2
7.1 ?? (1)

• ??? (Cartesian product) ??? ????????????
• ?????????? (Cartesian product) ?
• ??? ?? ?????????????????,????
• ??

3
??7.1????

• ????????????
• ???
• ? X ? Y ????????,??? ????? ? ?????
  ????????,????

4
??7.2????

• ???????????????
• ??? X ? Y ?????,?? R ???? X ? Y ???x ???
  y,??????????????????
• ?? X3,4,5,6 ??Y3,4,5,????????????????????

5
7.1 ?? (2)

• ????????????,??????????????????????????,??????????
  ??????????????? R?S?? T ????? ,????
• 1. ??
• 2. ??
• 3. ??
• 4. ??

6
7.2 ??????? (1)

• ????? R ??? X ? Y????????,?? R ? X ? Y
  ???,?????
• ??? ?
  ?????? X ? Y ?????(???),??????????????

?7.1?????????
7
7.2 ??????? (2)

• ?????? ?R???X?Y???????????,????X ?
  Y?????????????
• ??? ???? X ?
  Y????????,????????,??????

?7.2???????????
8
??7.3??(binary)????????????

• ???????R?????,????? ,???

9
??7.4??(ternary)???????????? (1)

• ???????????????
• ? ?? R ??? X1 X X2??????,????,
  ?

( x , a ) max(0.9,0) 0.9
( x , b ) max(0.4,0) 0.4
( y , a ) max(1,0.7) 1
( y , b ) max(0,0.8) 0.8
10
??7.4?????????????? (2)

• ? R3 ?? R ??? X3 ??????,
  ,?
• ?R12?? R12 ?????
  ??????,R3 ?? R3 ?????
  ??????,??

(x3)
(s) max(0.9,0.4,1,0) 1
(t) max(0,0,0.7,0.8) 0.8


( x , a , s ) 0.9 1
( x , a , t ) 0.9 0.8
( x , b , s ) 0.4 1
( x , b , t ) 0.4 0.8
( y , a , s ) 1 1
( y , a , t ) 1 0.8
( y , b , s ) 0.8 1
( y , b , t ) 0.8 0.8
11
7.3 ???? (1)

• ??????????????????(composition),?????????(relat
  ion-relation)?????????(set-relation)????
• ??????????,?????-????(max-min operation)???????
• ? P ? Q ?????? ?
  ????????,?????????????,? P ? Q ??????
  ?????? R,???????

12
??7.5???????

• ???????????
• ??
• ?P?Q????

13
7.3 ???? (2)

• ? ? ???????
  ? ???????,??P ? Q ?????????
• ?? t(. , .) ???????????-????(max-min
  operation)?????? P ? Q ???

14
??7.6???????

• ??????????????
• ????? P ????? Q ????

15
????????????

• ? A ???? X ????????,R ???? X ? Y ????????,??????
  ?????? A ????? R ???,???
• ???????,A ? R ???????? Y ?????? B?
• ????????????????????????,?????(max)???(min)
  ??????,???????????? t-conorm ? t-norm ????
• ??,????????????????????,???-????(max-min
  operation)????????????

16
7.4 ???? (1)

• ??????????????????????????????
• ???????????? Zadeh ?1975???????
• ?????????????, ,?? x
  ??????,T(x)? x ????(term set),????? x
  ???????????,???? x ????(linguistic value), U ?x
  ???, G ??? x ?????????(syntactic rule),? M ?? x
  ?????????????????????(semantic rule)?

17
??7.7?????

• ????????????????,?? x ??,?????????????
• ?? U ???? 0, 50 ??????? T(x) ????? G
  ??????????,???????????,????????????,??????????
  ?????? M ????????????????,???
• M(?) ????10?????,?????? ?
• M(?) ????25?????,?????? ?
• M(?) ????35?????,?????? ?

?7.3????????????,???????????
18
??????? (1)

• ??CON(A)
• ??DIL(A)
• ??INT(A)
• ???????,??????????????
• ??(A) highly(A) A3
• ?(A) very(A) CON(A) A2
• (A) more or less(A) DIL(A) A0.5
• ??(A) roughly(A) A0.25
• ??(A) rather(A) INTCON(A)AND
  NOTCON(A)

19
??????? (2)

• ???? A ? x ??? 0 ?????

?7.4???????????
20
7.4.2 ???? (1)

• ????(fuzzy rule) ????????????
• ???? If x is A
  Then y is B
• ???A?B????????X?Y???????
• x is A ???????????(antecedent or premise),?y
  is B????????????(consequence or conclusion) ?
• ????????????????
• ???? If x is A
  Then y is B
• ???,?????????????????(crisp implication)
  A?B ,??????? (propositional implication),???????
  ?(truth) ?? (false)?

21
7.4.2 ???? (2)

• ?? A?B ? ? ?????
• ???????????????,??????? ? ? ? ??
  ????????????????????????

A B A?B
T T T T T
T F F F F
F T T T T
F F T T T
22
7.4.2 ???? (3)

• ?????????????????,?????????,??????????
• Dienes-Rescher Implication
• Lukasieweicz Implication
• Zadel Implication
• Godel Implication

23
7.4.2 ???? (4)

• If x is A Then y is B
  may be interpreted as
• If x is A Then y is B
  Else nothing
• ?? A?B ? ?????
• Mamdani Implication
• Product Implication

24
7.5 ???? (1)

• ????????,????????? ? modus ponens
• ??? (premise 1)x is A
• ??? (premise 2)If x is A
  Then y is B
• -----------------------------
  -------------------------------
• ??y is B
• ? modus ponens ???????????,????
• ??? (premise 1)x is A
• ??? (premise 2)If x is A
  Then y is B
• -----------------------------
  -------------------------------
• ??y is B
• ?? A ? B??????? A ? B ?????,???????????
  generalized modus ponens (???GMP) ?

25
???????(compositional rule of inference)
26
???????(1)
27
??????? (2)

• ???? A ????? C(A) ??????
• ???? C(A)?R ??????
• ? C(A)?R ??? Y ?,??
• ??????????????

28
??????? (3)

• ???? ??????????
• ?? ? ????????
• ??????????????
• ??? A?A??? B ?????? X?X?? Y ??????,
• ???? If x is A Then y is B
  ??????????? A?B ???,
• ????????????????,??????
• ?????????-????,????????

29
7.5.1 ????,???? (1)

• ?? x is A
• ????If x is A, Then y is B
• ------------------------------------------------
• ?? y is B
• ????? A?B ??Mandani? RM ???,????
• ?
• ?? ? ???????????????,????????(firing
  strength)? ?
  ????????????

30
7.5.1 ????,???? (2)

• ????? A ?????? (fuzzy singleton),???
• ?

? 7.7?????????????????
31
7.5.2 ???,???? (1)

• ?? x is A
• ???? R1 If x is A1, Then y is B1
• ???? RJIf x is AJ, Then y is BJ
• --------------------------------------
  --------------------
• ?? y is B
• ?? ,??

32
7.5.2 ???,???? (2)

• ?? ?i ???i??????????
• ????? ?????? ,?

33
?7.8????????????????
34
7.5.3 ????,??? (1)

• ?? x is A and y is B
• ????If x is A and y is B Then z is C
• -------------------------------------------
  -------------------
• ?? z is C
• ?????????????? ?????????
  
• ???????? C ?

35
7.5.3 ????,??? (2)

• ?? ?A ? ?B ???? A ? A ? B ? B
  ????????(degree of compatibility)?
  ??????????????
• ???????

36
????? A ? B ?????,?? A x0 ?? B y0 ,?
??
? 7.9????????????????
37
7.5.4 ???,??? (???)

• ?? x is A and y is B
• ???? R1 If x is A1 and y is B1 Then
  z is C1 Else
• ???? R2 If x is A2 and y is B2 Then z
  is C2 Else
• ???? RJ If x is AJ and y is BJ Then z
  is CJ
• -------------------------------------------
  ------------------------------------
• ?? z is C
• ?? Ai? Bi ??? Ci ?????? X?Y?? Z ??????,?
  Else ????? ????,??

38
7.5.4 ???,??? (???)

• ?? ?Ai ? ?Bi???? Ai ? Ai ? Bi ? Bi
  ???????,? ?I ???? I ???????????

39
????? A ? B ?????,?? A x0 ?? B y0 ,?
??
?7.10???????????????