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)
