On generalized fuzzy relation equations: necessary and sufficient conditions for the existence of solutions

Esko Turunen

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Displaying similar documents to “On generalized fuzzy relation equations: necessary and sufficient conditions for the existence of solutions”

Equivalent fuzzy sets

Branimir Šešelja, Andreja Tepavčević (2005)

Kybernetika

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Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Relationship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.

A context-based approach to linguistic hedges

Martine De Cock, Etienne Kerre (2002)

International Journal of Applied Mathematics and Computer Science

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We present a framework of L-fuzzy modifiers for L being a complete lattice. They are used to model linguistic hedges that act on linguistic terms represented by L-fuzzy sets. In the modelling process the context is taken into account by means of L-fuzzy relations, endowing the L-fuzzy modifiers with a clear inherent semantics. To our knowledge, these L-fuzzy modifiers are the first ones proposed that are suitable to perform this representation task for a lattice L different from the...

A fuzzy version of Tarski's fixpoint theorem

Abdelkader Stouti (2004)

Archivum Mathematicum

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A fuzzy version of Tarski’s fixpoint Theorem for fuzzy monotone maps on nonempty fuzzy compete lattice is given.

Similarity in fuzzy reasoning.

Frank Klawonn, Juan Luis Castro (1995)

Mathware and Soft Computing

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Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval...