Abstract
In this study, an exact analytical inversion procedure is presented for interval type-2 Takagi–Sugeno–Kang fuzzy logic systems (IT2 TSK FLSs) with closed form inference methods. In this inversion procedure, the inversion variable is needed to be defined by piecewise linear interval type-2 fuzzy sets (PWL IT2 FSs). This provides a way to define an IT2 TSK FLS in a form that is composed of several fuzzy subsystems with respect to the inversion variable. In the proposed procedure, the output definitions of fuzzy subsystems are derived in a unique parametric form in terms of the inversion variable by using parameters of linear definition of membership functions. By rearranging this definition with respect to the inversion variable; either a linear, quadratic or cubic equation is obtained depending on the types of the inference method and rule consequents of the IT2 TSK FLS. Since explicit analytical solutions are available for these types of equations, the exact inverse solution(s) of each fuzzy subsystem can easily be calculated. The inverse solution set of overall IT2 TSK FLS is obtained by composing the inverse solutions of all fuzzy subsystems. The exactness and feasibility of the proposed inversion procedure has been illustrated through simulation examples.
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