Automatic Methods for Generation of Type-1 and Interval Type-2 Fuzzy Membership Functions

Abstract

Generation of membership functions is an important step in construction of fuzzy systems. Since membership functions reflect what is known about the variables involved in a problem, when they are correctly modeled the system will behave in the manner that is expected in the context of the problem being addressed. Since their creation, type-1 membership functions have been used in domains characterized by uncertainty. Nevertheless, use of type-2 membership functions has been expanding over recent years because they are considered more appropriate for this application. Both types of membership function can be generated with the aid of automatic methods that implement generation of membership functions from data. These methods are convenient for situations in which it is not possible to obtain all the information needed from an expert or when the problem in question is complex. The aim of this study is to present a review of the most important automatic methods for generation of membership functions, both type 1 and interval type-2, highlighting the principal characteristics of each approach.