Robustness of interval type-2 fuzzy logic systems

Fuzzy logic systems (FLSs) have been successfully used in various modeling and control applications. More importantly, we are witnessing an increasing interest in using interval type-2 FLSs (IT2 FLSs) for numerous applications. However, robustness, defined as the tolerance of an FLS to handle a maximum desired output deviation, is not usually considered in the design process of FLSs, and hence there is a need for an in-depth investigation. In this paper, we present a methodology for the robustness analysis of IT2 FLSs. Our approach is general and can be used to analyze the robustness of T1 FLSs as well. To demonstrate the effectiveness of the proposed methodologies, two examples are presented, and it is concluded that T1 and IT2 FLSs exhibit robust behaviors. Moreover, IT2 FLSs due to their flexible structures, revealed reduced output errors and in some cases showed enhanced robust performance than T1. In general, the superiority in terms of the robust performance of T1 over IT2 (or IT2 over T1) is problem-dependent. The approach presented in this paper can be exploited in the design of robust FLSs for modeling applications.