Fuzzy Logic

Abstract

Set is defined as a collection of entities that share common characteristics. From the formal definition of the set, it can be easily determined whether an entity can be member of the set or not. Classically, when an entity satisfies the definition of the set completely, then the entity is a member of the set. Such membership is certain in nature and it is very clear that an entity either belongs to the set or not. There is no intermediate situation. Thus, the classical sets handle bi-state situations and sets membership results in either ‘true’ or ‘false’ status only. These types of sets are also known as crisp sets. In other words, a crisp set always has a pre-defined boundary associated with it. A member must fall within the boundary to become a valid member of the set. An example of such classical set is the number of students in a class, ‘Student’. Students who have enrolled themselves for the class by paying fees and following rules are the valid members of the class ‘Student’. The class ‘Student’ is crisp, finite and non-negative. Here are some types of crisp sets.