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Type-2 Intervals of Constant Height

By Carol L. Walker and Elbert A. Walker


The algebra of truth values for fuzzy sets of type-2, due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting subalgebras, some of which could possibly serve as a basis of a useful fuzzy set theory. This paper is about such a subalgebra, one which generalizes the truth value algebra of intervalvalued fuzzy sets. We investigate it as an algebra, and determine its automorphism group. In particular, we show that is it a characteristic subalgebra and that its automorphisms are exactly those induced by automorphisms of the containing truth value algebra of fuzzy sets of type-2. Key words set Fuzzy truth values, type-2 fuzzy set, interval-valued fuzzy

Year: 2013
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