Combining the -Plane Representation with an Interval Defuzzification Method

Abstract

This paper is concerned with the defuzzification of the discretised generalised type-2 fuzzy set. In 2008 Liu proposed the α-Plane Representation — a decomposition of the generalised type-2 set into horizontal slices termed ‘α-planes’. An α-plane is akin to an interval type-2 fuzzy set. The α-Plane Representation must be used in conjunction with an interval defuzzification method: The three main options are 1. the Karnik-Mendel Iterative Procedure, 2. the Greenfield-Chiclana Collapsing Defuzzifier, or 3. the Nie-Tan Method. The experiments recorded in this paper address the question, “Which is the best interval defuzzification method for the α-Plane Representation to be combined with?”