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Automorphisms of algebras of fuzzy truth values

By Carol L. Walker and Elbert A. Walker


The truth values of type-2 fuzzy sets are fuzzy subsets of the unit interval. This set is endowed with some algebraic operations, and the resulting algebra has been studied rather extensively. Here we begin the study of automorphisms of this algebra. The set of automorphisms of an algebra forms a group, and often tells much about the structure and properties of the underlying algebra and identi es subalgebras of particular interest. Of special interest are those subalgebras that are carried onto themselves by automorphisms of the containing algebra, that is, the so-called characteristic subalgebras. Our chief concern here is identifying some of these characteristic subalgebras

Topics: Type-2 fuzzy sets, automorphisms 1. The Algebra of Fuzzy Truth Values
Year: 2006
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