## 7 December 2022

### Difference Between Fuzzy Set and Crisp Set

Fuzzy sets are set whose elements have degrees of membership, while crisp sets are sets whose elements have binary membership. Let us discuss some more Differences between the fuzzy set and crisp set with the help of the comparison given below.

What is a fuzzy set?

A fuzzy set is a collection of elements with varying degrees of membership in the set. In this context, fuzzy refers to ambiguity, in other words, the transition between various degrees of membership implies that the limits of the fuzzy sets are ambiguous, as a result, the membership of the universal elements in the set is measured against a function to identify the uncertainty and ambiguity.

What is Crisp Set?

The crisp set is a collection of objects (say, U) that have the same accountability and finiteness properties. A crisp set B is a group of elements over the universal set U. Where a random element may or may not be a part of B. That is there are only two possibilities, either the element belongs to set B or it does not belong to set B. The following equation is used to define the crisp set B, which contains a group of some elements in U that have the same property P.

## Difference between the Fuzzy set and the Crisp set:

• The fuzzy set defines the value between 0 and 1 including both 0 and 1. While the crisp set defines the value as either 0 or 1.
• A fuzzy set specifies the degree to which something is true. While the Crisp set is also called a classical set.
• Fuzzy ser shows partial membership. The crisp set shows full membership.
• The fuzzy set is used in the fuzzy controller. The crisp set application is used for digital design.
• A fuzzy set is infinite value function logic. While the Crisp set is bi-valued function logic.
• A fuzzy set is partial membership means true to false, yes to no, 0 to1. While the crisp set is a full membership means totally true/false, 0/1.
• A fuzzy set is determined by its indeterminate boundaries, there exists uncertainty about the boundaries. A crisp set is defined by crisp boundaries and contains the precise location of the set boundaries.
• There are several applications of the crisp and fuzzy set theory, but both are driven toward the development of efficient expert systems.
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