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What is Type-2 Fuzzy Set & System

Chapter 1
Handbook of Research on Computational Intelligence for Engineering, Science, and Business
A type-2 fuzzy set maps elements in a crisp domain to type-1 fuzzy numbers bounded in the range [0,1]. We denote a fuzzy set as type-2 by placing a tilde character above the name of the set. Since the value at each point in a type-2 fuzzy set is given as a function, type-2 fuzzy sets are three-dimensional. Such sets can be used in situations where there is uncertainty about the membership grades themselves, e.g., an uncertainty in the shape of the membership function or in some of its parameters. Type-2 fuzzy sets and systems generalize (type-1) fuzzy sets and systems so that more uncertainty can be handled.
Published in Chapter:
Computational Intelligence Using Type-2 Fuzzy Logic Framework
A. Neogi (The University of Burdwan, India), A.C. Mondal (The University of Burdwan, India), and S.K. Mandal (National Institute of Technical Teachers’ Training & Research, India)
Copyright: © 2013 |Pages: 29
DOI: 10.4018/978-1-4666-2518-1.ch001
Abstract
In this chapter, the authors expand the notion of type-2 fuzzy sets. An introduction to standard and interval (type-2) fuzzy sets and systems is explained in the early part of the discussion. The chapter also covers the ideas of hybrid type-2 fuzzy system. Next, the authors study the applicability of type-2 fuzzy logic (FL) system in student’s performance in oral presentation as it is clearly new field of research topic and have an excellent opportunity to combine several fuzzy set method developed in the recent years. The proposed application shows the linkage of type-2 fuzzy system with TOPSIS. The present chapter also highlights the possible future directions for type-2 FL system research. By the end of the chapter, the authors hope that even those with little previous experience of fuzzy logic should be enabled to apply these methods in their own application areas and/or begin research in this fascinating and exciting area.
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