Designing Fuzzy Sets With the Use of the Parametric Principle of Justifiable Granularity

This study is concerned with a design of membership functions of fuzzy sets. The membership functions are formed in such a way that they are experimentally justifiable and exhibit a sound semantics. These two requirements are articulated through the principle of justifiable granularity. The parametric version of the principle is discussed in detail. We show linkages with type-2 fuzzy sets, which are constructed on a basis of type-1 fuzzy sets. Several experimental studies are reported, which illustrate a behavior of the introduced method.