Difference Between Fuzzy Set and Crisp Set

In this post, we will understand the difference between fuzzy set and crisp set −

Fuzzy Set

• It is understood using vague properties.

• Fuzzy set can have a progressive transition among many degrees of membership.

• They are generally used in fuzzy controllers.

• The elements have the ability to be partially included in the set.

• They are based on infinite-valued logic.

• They exhibit gradual membership degrees.

• There is an uncertainty about the set boundaries.

Crisp Set

• It can be understood using precise and certain characteristics.

• Here, the transition is sudden, and well defined, not gradual.

• The element can either be a member of a set or not, no partial ability given.

• It has a digital design.

• It is based on bi-valued logic.

• They can have a total membership or non-membership.

• It has a precise location for the set boundaries.