Fuzzy Logic in Soft Computing

In our day to day life, we use those terms which are imprecise in nature. It rains heavily. Boy is Good. Whether is cloudy. The question is How much?

Fuzzy deals with handling of this imprecise theory.

Stochastic Uncertainty: (80%)
Lexical Uncertainty: Tall man, hot days, stable currencies.

Conventional Boolean Set Theory:
The answer is 0 or 1.
The crisp boundary is framed

Fuzzy Set Theory:
The answer is varied in between 0 and 1
The boundary is gradual.

Fuzzy Logic: Reasoning with qualitative information
Fuzzy set differs from crisp set in terms of membership

Membership/ Character/ Discriminative predicate

x={1,2,3,4,6,8,10}
u belongs to x.
u is membership function of x which is either 1 or 0. // for crisp set

Us is between 0 and 1 (both are included) // for fuzzy set
Characteristic function: 0 <=Us<=1

Notion of truth can be modeled in fuzzy set
Member functions represent curves

Alpha-cut is a crisp set whose values are greater than 0.
Union: Maximum of both
Intersection: Minimum of both

Converting a fuzzy term in crisp value is called defuzzification