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A FAMILY OF FINITE DE MORGAN AND KLEENE ALGEBRAS

CAROL L. WALKER

Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, USA

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and

ELBERT A. WALKER

Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, USA

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https://doi.org/10.1142/S0218488512500298Cited by:5 (Source: Crossref)

Abstract

The algebra of truth values for fuzzy sets of type-2 consists of all mappings from the unit interval into itself, with operations certain convolutions of these mappings with respect to pointwise max and min. This algebra generalizes the truth-value algebras of both type-1 and of interval-valued fuzzy sets, and has been studied rather extensively both from a theoretical and applied point of view. This paper addresses the situation when the unit interval is replaced by two finite chains. Most of the basic theory goes through, but there are several special circumstances of interest. These algebras are of interest on two counts, both as special cases of bases for fuzzy theories, and as mathematical entities per se.

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