. , .
, .
: (Fuzzy conjunction fuzzy AND).
:
= ,
- A, B .
: : (Fuzzy disjunction fuzzy OR). :
= ,
- A, B .
: (Fuzzy negation). :
= ,
- A.
(Fuzzy implication a fuzzy rule) :
, ,
A B - , C U . : .
Ȼ ( A) (the antecedent) . λ ( ) (consequence) .
: (Fuzzy implication). :
= ,
(fuzzy AND operation) - .
, , (Mamdani implication).
. 2.9 R.
() | () |
. 2.9.(, )
(. 2.9 ()) : . (. 2.9,) , :
. R
= A B = ,
* (fuzzy AND operator), ..
= .
. , / .
. , . , - -. :
(Lukasiewiczs implication):
= ;
(Larsen implication):
= ;
(Zadeh implication):
= .
:
|
|
.
, , (reasoning process) , . 2.10.
. . 2.10 :
Current data ;
Reasoning scheme ;
KB (Knowledge Base) ; A set of Rules- ;
New Facts .
. 2.10.
, , (inference), :
1. (matching) (A1,A2,) , ,
2. (Inferring) () (B1, B2,) .
.
(classical propositional logic) . (modus ponens) (modus tollens), .
Modus ponens : ,
: Y Y =A, , B .
, , , , ().
Modus tollens : ,
: Y = ( ), , , .
, , :
(Law of syllogism): ;
(Law of contra positive): ;
(Law of double negation): .
modus ponens :
1 ( ):
: ,
:
:
(exact matching) () ();
(/) .
. 2.11.
( ) .
. (generalized modus ponens):
,
: (), ().
:
1 ( ):
: ,
:
. 2.11.
, .
(approximate matching) () ();
(continuous-valued truth values) .
|
|
: , ?
, max-min
, .
- X R - X Y: .
:
1 ( ):
: ,
:
: Y.
.
, . , R .
:
1. (cylindrical extension) . . , X X Y.
2. R, .. .
3. Y. Y.
.
, , , , .
= .
.
, Y, ( ):
= = . (2.1)
(2.1) max-min (max-min composition). :
. (2.2)
( ), max-product :
= . (2.3)
(2.1) (2.3) .
: , . , :
: ,
.
(2.2) :
= .
= = =
= . (2.4)
- .
. a firing strength of a rule, . .
: , . :
.
R,
(2.5)
:
= (2.6)
(2.5) (2.2) (2.6), :
=
(2.7)
(2.7) . 2.12.
. 2.12. max-min
(2.7), . 2.12. ( ) : A , B and . . C .
. :
.
w w1 w1.
: , . :
|
|
1 (): , and ,
1:
2:
():
. 2.13.
:
= (2.8)
max-min , (2.8) :
= =
, (2.9)
and - 1 2.
, (.. ) .
(2.9) . 2.13.
(min-max) .