Tutorial on the uses of the interval type-2 fuzzy set’s Wavy Slice Representation Theorem

Abstract

This tutorial paper demonstrates how the Wavy Slice Representation Theorem (RT) for a general type-2 fuzzy set (T2 FS), when specialized to an interval T2 FS (IT2 FS), can be used as the starting point to solve many diverse problems that involve IT2 FSs. The problems considered are: Set theoretic operations, centroid, uncertainty measures, similarity, inference engine computations for Mamdani IT2 fuzzy logic systems, and linguistic weighted average. Each solution obtained from the RT is a structural solution but is not a computational solution, however the latter are always found from the former. It is this author's recommendation that one should use the RT as a starting point whenever solving a new problem involving IT2 FSs, because it has had such great success in solving so many such problems in the past.