Type-2 Fuzzy Sets Including Word Models

This chapter formally introduces type-2 fuzzy sets and is the backbone for the rest of this book. It includes a lot of new terminology and also a way to obtain a type-2 fuzzy set model for a word. The coverage of this chapter 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, and also modeling secondary membership functions; how to represent non-type-2 fuzzy sets as type-2 fuzzy sets; returning to linguistic labels for type-2 fuzzy sets; multivariable membership functions; and interval type-2 fuzzy set word models, including such models for two vocabularies (one with 32 words, and the other with 16 words). The appendix provides sources for other word codebooks. Twenty-six examples are used to illustrate the important concepts.