Displaying similar documents to “Distributivity of ordinal sum implications over overlap and grouping functions”

Scalar cardinalities for divisors of a fuzzy cardinality.

Juan Casasnovas Casasnovas (2002)

Mathware and Soft Computing

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The cardinality of a finite fuzzy set can be defined as a scalar or a fuzzy quantity. The fuzzy cardinalities are represented by means the generalized natural numbers, where it is possible to define arithmetical operations, in particular the division by a natural number. The main result obtained in this paper is that, if determined conditions are assured, the scalar cardinality of a finite fuzzy set, B, whose fuzzy cardinality is a rational part of the fuzzy cardinality of another fuzzy...

On types of fuzzy numbers under addition

Dug Hun Hong (2004)

Kybernetika

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We consider the question whether, for given fuzzy numbers, there are different pairs of t -norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.

Towards the properties of fuzzy multiplication for fuzzy numbers

Alexandru Mihai Bica, Dorina Fechete, Ioan Fechete (2019)

Kybernetika

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In this paper, by using a new representation of fuzzy numbers, namely the ecart-representation, we investigate the possibility to consider such multiplication between fuzzy numbers that is fully distributive. The algebraic and topological properties of the obtained semiring are studied making a comparison with the properties of the existing fuzzy multiplication operations. The properties of the generated fuzzy power are investigated.

Parametric families of fuzzy consequence operators.

Javier Elorza, Pedro Burillo (2004)

Mathware and Soft Computing

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In a previous paper we explored the notion of coherent fuzzy consequence operator. Since we did not know of any example in the literature of non-coherent fuzzy consequence operator, we also showed several families of such operators. It is well-known that the operator induced by a fuzzy preorder through Zadeh's compositional rule is always a coherent fuzzy consequence operator. It is also known that the relation induced by a fuzzy consequence operator is a fuzzy preorder if such operator...

Fuzzy morphological operators in image processing.

Pedro J. Burillo López, Noé Frago Paños, Ramón Fuentes González (2003)

Mathware and Soft Computing

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First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Lukasiewicz's one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout's manner) that satisfies the axioms of Divyendu and Dogherty. Second, we propose a method to define fuzzy morphological operators (erosions and dilations). A family...

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.

On completeness and direction in fuzzy relational systems.

Pedro J. Burillo López, Ramón Fuentes-González, León A. González Sotos (1998)

Mathware and Soft Computing

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The concepts of bounded subset, complete subset and directed subset, wich are well known in the context of partially ordered sets (X,≤), are extended in order to become appliable, with coherence, in fuzzy relational systems (X,R). The properties of these generalized structures are analyzed and operative exemples of them are presented.