Granular interval type-2 membership functions and modeling application on a nonlinear system

Abstract

There are various ways to interpret uncertainty on membership functions of interval type-2 fuzzy sets. In this study, Granular Interval Type-2 Membership Functions (GIT2 MFs) are introduced. The footprint of uncertainty of GIT2 MFs is formed by using rectangular interval type-2 fuzzy granules. GIT2 MFs provide more degrees of freedom and flexibility in design procedure of interval type-2 membership functions. Therefore, interval type-2 fuzzy logic systems using GIT2 MFs have more potential to model and handle uncertainties. By using GIT2 MFs, uncertainties on the grades of membership functions can be represented independently for any region in the universe of discourse. Thus, it provides the designer to form highly nonlinear, discontinuous or hybrid membership functions which are formed as a combination of type-1 and type-2 characteristics. This makes it possible to model any desired discontinuity and nonlinearity on the universe of discourse or in any input-output mapping. The effectiveness of the proposed GIT2 MFs is demonstrated through simulations on modeling a nonlinear system having dead zone. The simulation results show that the fuzzy system using proposed GIT2 MFs is superior to the fuzzy system using conventional interval type-2 membership functions.