Robustness of General Type-2 TSK Fuzzy Systems

Dhan Jeet Singh, Mohd Aquib, Teena Sharma, Nishchal K. Verma

Abstract: This article presents the robustness of General Type-2 fuzzy logic system (GT2 FLS) as an extension of interval type-2 (IT2) FLS. The theoretical base and mathematical derivations developed for robustness of IT2 FLS is extended for GT2 FLS using $\alpha$ -plane representation. The robustness analysis for computing the robustness index is modified for $\alpha$ level type-2 FLS and by aggregating all such levels, it is further customized for GT2 FLS. To demonstrate the efficacy of extended methodology, function approximation-based simulation examples are considered. It was understood that similar to T1 and IT2 FLS, the GT2 FLS can be developed to attain the robust performance with more flexible structure. The additional design flexibility associated with GT2 FLS provides reduced output error and enhanced robustness performance based on nature of application.