Displaying similar documents to “Yager’s classes of fuzzy implications: some properties and intersections”

Properties of fuzzy relations powers

Józef Drewniak, Barbara Pȩkala (2007)

Kybernetika

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Properties of sup - * compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider sup - * powers of fuzzy relations under diverse assumptions about * operation. At first, we remind fundamental properties of sup - * composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations...

Preservation of properties of fuzzy relations during aggregation processes

Józef Drewniak, Urszula Dudziak (2007)

Kybernetika

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Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n -ary operations is considered. Namely, with the use of fuzzy relations R 1 , ... , R n and n -argument operation F on the interval [ 0 , 1 ] , a new fuzzy relation R F = F ( R 1 , ... , R n ) is created....

Some properties of B -operations

Bohdan Butkiewicz (2007)

Kybernetika

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In the paper the problem of mathematical properties of B -operations and weak W B -operations introduced by the author for interpretation of connectives “and”, “or”, and “also” in fuzzy rules is considered. In previous author’s papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system described by set of rules of the type if – then. Monotonicity condition, required for triangular...

S -measures, T -measures and distinguished classes of fuzzy measures

Peter Struk, Andrea Stupňanová (2006)

Kybernetika

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S -measures are special fuzzy measures decomposable with respect to some fixed t-conorm S . We investigate the relationship of S -measures with some distinguished properties of fuzzy measures, such as subadditivity, submodularity, belief, etc. We show, for example, that each S P -measure is a plausibility measure, and that each S -measure is submodular whenever S is 1-Lipschitz.