Analysis of the FLC with shrinking span membership functions

This article aims to investigate the input-output parametric relationship of a class of crisp-type fuzzy logic controllers (FLCs) using various t-norm-sum-gravity inference methods. Two most frequently used t-norms, namely the standard intersection and the algebraic product, are applied in calculating the matching level of each control rule, and the summation operator and the center-of-gravity method are applied to evaluate the final crisp output. The explicit mathematical forms of reasoning surfaces are addressed. Reasoning surfaces of these crisp-type FLCs are proved to be composed of a two-dimensional multilevel relay, no matter which t-norm is used, and a local position-dependent nonlinear compensator with output pattern influenced by the t-norms selected