Journal
FUZZY SETS AND SYSTEMS
Volume 159, Issue 22, Pages 3014-3032Publisher
ELSEVIER
DOI: 10.1016/j.fss.2008.01.017
Keywords
Type-2 fuzzy logic; Fuzzy truth values; Fuzzy implications; Residuation
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In this paper we consider algebras of fuzzy truth values equipped with an implication operation. Generalizing the definition of type-1 fuzzy implications, we discuss extended fuzzy S-implications and coimplications and also extended residual implications and coimplications, in particular to the extended residual of minimum. We study the algebraic properties of these operations and their relationships to extended t-norms and t-conorms in particular to meet and join. These investigations are intended to provide a theoretical background for type-2 approximate reasoning applications. (C) 2008 Elsevier B.V. All rights reserved.
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