Difference Between Crisp Set and Fuzzy Set

Crisp Set: Countability and finiteness are identical properties which are the collection objects of crisp set. ‘X‘ is a crisp set defined as the group of elements present over the universal set i.e. U. In this case a random element is present that may be a part of X or not that means two ways are possible to define the set. These are first element would become from set X, or it does not come from X. 

Fuzzy Set: The Integration of the elements having a changing degree of membership in the set is called as fuzzy set. The word “fuzzy” indicates vagueness, On the other hand, we can say that the replacement among various degrees of the membership implies that the vague and ambiguity of the fuzzy set. Hence, the measurement of the membership of the elements from the universe in the set against a function for detecting the uncertainty and ambiguity.

S.No	Crisp Set	Fuzzy Set
1	Crisp set defines the value is either 0 or 1.	Fuzzy set defines the value between 0 and 1 including both 0 and 1.
2	It is also called a classical set.	It specifies the degree to which something is true.
3	It shows full membership	It shows partial membership.
4	Eg1. She is 18 years old. Eg2. Rahul is 1.6m tall	Eg1. She is about 18 years old. Eg2. Rahul is about 1.6m tall.
5	Crisp set application used for digital design.	Fuzzy set used in the fuzzy controller.
6	It is bi-valued function logic.	It is infinite valued function logic
7	Full membership means totally true/false, yes/no, 0/1.	Partial membership means true to false, yes to no, 0 to 1.

Crisp Set

Fuzzy Set

Conclusion:   

  The part of distinct set theories are fuzzy set and crisp set, where there are no-finite numbers of logic are implemented in fuzzy set while only two numbers of logic are implemented in crisp set.