Type-2 implications on non-interactive fuzzy truth values

doi:10.1016/j.fss.2008.01.017

Fuzzy Sets and Systems

Volume 159, Issue 22, 16 November 2008, Pages 3014-3032

https://doi.org/10.1016/j.fss.2008.01.017 Get rights and content

Abstract

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.

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Type-2 implications on non-interactive fuzzy truth values

Abstract

Equations with fuzzy numbers

Inform Sci.

On the relationship between some extensions of fuzzy set theory

Fuzzy Sets and Systems

Operations on fuzzy numbers

Internet. J. Systems Sci.

Operations in a fuzzy-valued logic

Inform. and Control

On fuzzy implication operators

Fuzzy Sets and Systems

Fuzzy Preference Modelling and Multicriteria Decision Support

Operations on type-2 fuzzy sets

Fuzzy Sets and Systems