Play with fuzzy sets

 PLAY WITH  FUZZY  SETS :

A set or a crisp set is defined  as a 

collection of elements . The elements are 

either a member or not a member of the 

set . But Fuzzy sets are more flexible in 

approach  as compared  to the sets .

Fuzzy set can be viewed as an 

extension & generalization 0f  the 

basic concepts of crisp set .It supports 

flexible sense of membership with a 

parameter called "membership  degree" . 

It is multivalued between 0 and 1 (both 

included). You  will be  surprised  to 

know that Fuzzy logics donot follow 

LAW  OF EXCLUDED MIDDLE & LAW 

OF CONTRADICTION .If  we will choose 

fuzzy union & intersection that will 

follow these law then , the operations 

will not satisfy distribution and 

idempotence .

LAW  OF EXCLUDED MIDDLE states 

that for any proposition , either that 

proposition is true , or its negation is 

true .
LAW  OF CONTRADICTION  states that 

two antiethical propositions cannot be 

true at the same time . For example - X 

cannot be NOT X simultaneously.
Distributive property :-
                        5(x+30) = 5x + 150 
Idempotence property :-
                          op( op(x)) == op(x)