On the justification to use a novel simplified interval type-2 fuzzy logic system

Abstract

Wu-Mendel Uncertainty Bounds (WM UB) is a viable inference engine for interval type-2 fuzzy logic systems (IT2 FLS). This engine; however, has a complex structure and hence performing analysis using this mechanism is difficult. Moreover, when WM UB is used for control, one cannot guarantee stability. As such, a new IT2 FLS, called an m–n IT2 FLS, that is a simplified version of the WM UB IT2 FLS, has been recently introduced in the literature. The m–n IT2 FLS has enabled rigorous analyses of IT2 fuzzy controllers, has recently been used in several applications and has shown great promise to be used as a viable IT2 FLS that is not limited just to control. In this paper, we mathematically analyze the structure of the m–n IT2 FLS and through bounds approach find the conditions upon which the m–n IT2 FLS gets close to the WM UB. These conditions will also provide guidelines for the design parameters of the m–n IT2 FLS that will ultimately help designers to choose these parameters for their applications. The results presented in this paper should lead to wider applications of the novel and simplified m–n IT2 FLS.