Type-2 Fuzzy Sets and Systems: a Retrospective

Abstract

This article provides a high-level retrospective of type-2 fuzzy sets and fuzzy logic systems. It explains how type-2 fuzzy sets can be used to model membership function uncertainties, and how by doing this smoother performance can be obtained than by using type-1 fuzzy sets. It also summarizes the notation that should be used for type-2 fuzzy sets, describes four important mathematical representations for these fuzzy sets, explains the differences between type-1 and type-2 fuzzy logic systems and which of the four representations is most useful when designing an optimal type-2 fuzzy logic system, provides a very useful strategy for optimal designs of fuzzy logic systems – one that guarantees performance improvement as one goes from a type-1 fuzzy logic system to a type-2 fuzzy logic system design – , and describes four methods for simplifying the designs of type-2 fuzzy logic systems. Finally, it explains why type-2 fuzzy sets can capture two kinds of linguistic uncertainties simultaneously (the uncertainty of an individual and the uncertainties of a group about a word), whereas type-1 fuzzy sets cannot, and that such type-2 fuzzy set word models are what should be used to implement Zadeh’s Computing With Words paradigm.