Mathematical Foundations of Fuzzy Sets

2Fuzzy Sets

The main idea of fuzzy sets is to consider the degree of membership. A fuzzy set is described by a membership function that assigns to each member or element a membership degree. Usually, the range of this membership function is from 0 to 1. A degree of 1 represents complete membership to the set, and degree of 0 represents absolutely no membership to the set. A degree between 0 and 1 represents partial membership to the set.

We can define high fever as a temperature higher than 102 . Even if most doctors will agree that the threshold is at about 102 , this does not mean that a patient with a body temperature of 101.9 does not have a high fever while another patient with 102 does indeed have a high fever. Therefore, instead of using this rigid definition, each body temperature is associated with a certain degree. For example, we show a possible description of high fever ...