## Abstract

This chapter introduces a computation called *type*-*reduction* that lets a type-2 fuzzy set (T2 FS) be projected into a type-1 fuzzy set. Type-reduction is often used in a type-2 fuzzy system as a first step in going from a T2 FS to a number. Coverage includes: the interval weighted average (IWA), because it is the basic building block for type-reduction; three algorithms (KM, EKM, and EIASC) for computing the IWA; centroid type-reduction for interval T2 FSs and systems; height and center-of-sets type-reduction for IT2 fuzzy systems; centroid type-reduction for general T2 FSs and systems; height and center-of-sets type-reduction for GT2 fuzzy systems; an appendix that presents (for historical reasons) the early approach to type-reduction; and, an appendix about the mathematical properties of the IWA, and about continuous algorithms for performing centroid type-reduction. Fourteen examples are used to illustrate the important concepts.

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