Crisp-type fuzzy logic controller using Dubois and Prade´s parametric t-norm-sum-gravity inference methods

The input/output relationship of a class of crisp-type fuzzy logic controllers (FLCs) using parametric t-norm-sum-gravity inference method is examined. The explicit mathematical form of reasoning surface using Dubois and Prade´s parametric t-norm is addressed. Reasoning surfaces of crisp-type FLCs are proved to be composed of a two-dimensional multilevel relay and a local position-dependent nonlinear compensator. The influence of the α value, the parameter of Dubois and Prade´s parametric t-norm, on the reasoning surfaces is also investigated