Uncertain Rule-Based Fuzzy Systems pp 307-383 | Cite as

# Working with Type-2 Fuzzy Sets

## Abstract

This chapter explains how to work with type-2 fuzzy sets (T2 FSs). Most of its topics are needed in the rest of this book. Coverage includes: set-theoretic operations (union, intersection, and complement) for general type-2 fuzzy sets (GT2 FSs) computed using the Extension Principle, set-theoretic operations for interval type-2 fuzzy sets (IT2 FSs), set-theoretic operations for GT2 FSs computed using horizontal slices, type-2 relations and compositions on the same product space and on different product spaces, compositions of a T2 FS with a type-2 relation, type-2 hedges, Extension Principle for IT2 and GT2 FSs, functions of GT2 FSs computed using \( \alpha \)-planes, Cartesian product of T2 FSs, implications, an appendix about the properties of T2 FSs and an appendix that has detailed proofs of many theorems. 27 examples are used to illustrate the chapter’s important concepts.

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