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Transitivity of fuzzy relations under discretization
(2013-07-10)
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Article.
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Fuzzy transitivity is a key property for many fuzzy relational structures, such as fuzzy preorders and equivalences. Theoretical models for practical problems which are based on fuzzy relations make use of continuous scales, ...
Permutable fuzzy consequence and interior operators and their connection with fuzzy relations
(2015-07-20)
Article.
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Article.
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Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order ...
Indistinguishability operators with respect to different t-norms
(2012-04)
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An isomorphism f between two continuous Archimedean t-norms T and T′ transforms a T-indistinguishability operator E into a T′-indistinguishability operator f ∘ E and many interesting properties of E are transfered to f ∘ ...
On the Induction of New Fuzzy Relations, New Fuzzy Operators and Their Aggregation
(Springer, 2013)
Article.
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Article.
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In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We ...
Aggregation operators and quadric hypersurfaces
(Springer, 2013)
Article.
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Article.
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Aggregation operators that are quadric hypersurfaces are studied. The interest lays in the fact that the most popular aggregation operators are indeed quadric hypersurfaces.
Transitive closure of interval-valued fuzzy relations
(2013-07)
Article.
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Article.
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In this paper are introduced some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive ...
Finite-valued indistinguishability operators
(2011-10)
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Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity ...
Comparison of different algorithms of approximation by extensional fuzzy subsets
(Springer, 2013)
Article.
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Article.
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How to approximate an arbitrary fuzzy subset by an adequate extensional one is a key question within the theory of Extensional Fuzzy Subsets. In a recent paper by the authors [19] different methods were provided to find ...
Permutable indistinguishability operators, perfect vague groups and fuzzy subgroups
(2012-08-01)
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Article.
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Permutability between T-indistinguishability operators is a very interesting property that is related to the compatibility of the operators with algebraic structures. It will be shown that the sup −T product E ∘ F of two ...
Permutability of fuzzy consequence operators and fuzzy interior operators
(2013)
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In this paper we study the permutability of the composition of fuzzy consequence operators (fuzzy closings) and fuzzy interior operators (fuzzy openings). We establish several characterizations and we show the relation of ...