On the Equivalence of Mamdani Model and Fast Calculation Method of Type-2 Fuzzy Inference Model

Abstract

This paper addresses properties of type-1 and type-2 fuzzy inference models. It first clarifies relationship between the Mamdani model and product-sum-gravity model from the point of view of equivalence. Second, the above relationship is applied to the type-2 fuzzy functional inference model. Finally, this paper shows that the inference results of the type-2 fuzzy functional inference model can be obtained by using the above relationship and property.