Slicing strategies for the generalised type-2 Mamdani fuzzy inferencing system

Abstract

As a three-dimensional object, there are a number of ways of slicing a generalised type-2 fuzzy set. In the context of the Mamdani Fuzzy Inferencing System, this paper concerns three accepted slicing strategies, the vertical slice, the wavy slice, and the horizontal slice or α-plane. Two ways of defining the generalised type-2 fuzzy set, vertical slices and wavy slices, are presented. Fuzzification and inferencing is presented in terms of vertical slices. After that, the application of all three slicing strategies to defuzzification is described, and their strengths and weaknesses assessed.