Journal ArticleDOI
Generalized compositions of fuzzy relations
Józef Drewniak,Krzysztof Kula +1 more
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The dependences between algebraic properties of the operation * and the induced sup - * composition are discussed and consequences of these results for compositions based on triangular norms, triangular conorms and uninorms are presented.Abstract:
We examine compositions of fuzzy relations based on a binary operation *. We discuss the dependences between algebraic properties of the operation * and the induced sup - * composition. It is examined independently for monotone operations, for operations with idempotent, zero or identity element, for distributive and associative operations. Finally, we present consequences of these results for compositions based on triangular norms, triangular conorms and uninorms.read more
Citations
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Journal ArticleDOI
Increasing, continuous operations in fuzzy max equations and inequalities
Zofia Matusiewicz,Józef Drewniak +1 more
TL;DR: The goal is to achieve the most general assumptions for which sets of solutions' systems of equations and inequalities are the union of lattice intervals and a method of determination of all minimal solutions in such systems is indicated.
Journal ArticleDOI
Properties of Atanassov's intuitionistic fuzzy relations and Atanassov's operators
TL;DR: The goal of this paper is to consider properties of Atanassov's intuitionistic fuzzy relations which were introduced by AtanASSov in 1986, a continuation of examinations by Pe@?kala on the interval-valued fuzzy relations.
Journal ArticleDOI
Properties of $$\text{max-}*$$fuzzy relation equations
Józef Drewniak,Zofia Matusiewicz +1 more
TL;DR: The max–min and max–prod composition is used for wide family of operations for finite fuzzy relation equations and families of solutions of two relation equations are compared.
Proceedings Article
Preservation of properties of interval-valued fuzzy relations
TL;DR: Some properties of interval matrices considered by Pekala (2007) on these of interval-valued fuzzy relations of fuzzy set theory are generalized.
Book ChapterDOI
Compositions of Fuzzy Implications
Józef Drewniak,Jolanta Sobera +1 more
TL;DR: This chapter considers fuzzy implications as a special case of fuzzy relations in [0,1] and examines compositions of fuzzy implications based on a binary operation ∗ and discusses the dependencies between algebraic properties of the operation∗ and the induced sup − ∗ composition.
References
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Book
The algebraic theory of semigroups
A. H. Clifford,G. B. Preston +1 more
TL;DR: A survey of the structure and representation theory of semi groups is given in this article, along with an extended treatment of the more important recent developments of Semi Group Structure and Representation.
Journal ArticleDOI
Similarity relations and fuzzy orderings
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
Journal ArticleDOI
L-fuzzy sets
TL;DR: This paper explores the foundations of, generalizes, and continues the work of Zadeh in [I] and [2].
Book
Fuzzy Preference Modelling and Multicriteria Decision Support
János Fodor,Marc Roubens +1 more
TL;DR: This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.