Type-reduction of the discretised interval type-2 fuzzy set

It is investigated mathematically what happens to the Representative Embedded Set Approximation as the domain discretisation becomes finer, which leads into a discussion of the relationship between the collapsing and Nie-Tan methods.

Abstract

We begin by surveying the available strategies for type-reducing a discretised type-2 fuzzy set to a type-1 fuzzy set, namely the exhaustive method, the Karnik-Mendel Iterative Procedure, the sampling method, the Greenfield-Chiclana Collapsing Defuzzifier and the Nie-Tan method. We go on to investigate mathematically what happens to the Representative Embedded Set Approximation as the domain discretisation becomes finer. This leads into a discussion of the relationship between the collapsing and Nie-Tan methods. An experimental comparison is made between the collapsing and Nie-Tan methods, with respect to both efficiency and accuracy.