Discuss difference between Crisp Set and Fuzzy Set

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


Crisp set defines the value is either 0 or 1

Fuzzy set defines the value between 0 and 1 including both 0 and 1.


It is also called a classical set.

It specifies the degree to which something is true.


It shows full membership

It shows partial membership.


Crisp set application used for digital design.

Fuzzy set used in the fuzzy controller.


It is bi-valued function logic.

It is infinite valued function logic


Full membership means totally true/false, yes/no, 0/1.

Partial membership means true to false, yes to no, 0 to 1.


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.  

Crisp Set

Fuzzy Set

The fuzzy set theory is intended to introduce the imprecision and vagueness in order to attempt to model the human brain in artificial intelligence and significance of such theory is increasing day by day in the field of expert systems. However, the crisp set theory was very effective as the initial concept to model the digital and expert systems working on binary logic.