Explain fuzzy set and crisp set. Mention applications of fuzzy logic

 crisp sets

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Crisp sets are the sets that we have used most of our life. In a crisp set, an element is either a member of the set or not. For example, a jelly bean belongs in the class of food known as candy. Mashed potatoes do not.

Fuzzy sets 

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Fuzzy sets, allow elements to be partially in a set. Each element is given a degree of membership in a set.

This membership value can range from 0 (not an element of the set) to 1 (a member of the set).

It is clear that if one only allowed the extreme membership values of 0 and 1, that this would actually be equivalent to crisp sets. A membership function is the relationship between the values of an element and its degree of membership in a set.

Applications

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Fuzzy sets are appropriate for pattern classification because a given gesture or pattern may in fact have partial membership in many different classes. Several companies already have products based on fuzzy pattern recognition:
1. Hand Writing Recognition: CSK, Hitachi
2. Hand Printed Character Recognition: Sony
3. Voice Recognition: Ricoh, Hitachi