Type-2 Fuzzy Sets

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Abstract

This chapter formally introduces type-2 fuzzy sets and is the backbone for the rest of this book. It includes a lot of new terminologies. Coverage includes: the concept of a type-2 fuzzy set, definitions of general type-2 fuzzy sets and associated concepts, definitions of interval type-2 fuzzy sets and associated concepts, examples of two popular footprints of uncertainty, interval type-2 fuzzy numbers, a hierarchy of different kinds of type-2 fuzzy sets, mathematical representations of type-2 fuzzy sets including the vertical slice, wavy slice, and horizontal slice representations, which mathematical representations are most useful for optimal design applications, how to represent non-type-2 fuzzy sets as type-2 fuzzy sets, returning to linguistic labels for type-2 fuzzy sets, and multivariable MFs. 24 examples are used to illustrate the important concepts.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA

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