Displaying similar documents to “A theorem for basis operators over intuitionistic fuzzy sets.”

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...

On four intuitionistic fuzzy topological operators.

Krassimir T. Atanassov (2001)

Mathware and Soft Computing

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Four new operators, which are analogous of the topological operators interior and closure, are defined. Some of their basic properties are studied. Their geometrical interpretations are given.

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...

On the generators of T-indistinguishability operator.

Joan Jacas (1988)

Stochastica

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The structure of the generators' set of a T-indistinguishability operator is analyzed. A suitable characterization of such generators is given. T-indistinguishability operators generated by a single fuzzy set, in the sense of the representation problem, are studied.

Generation of fuzzy mathematical morphologies.

Pedro J. Burillo López, Noé Frago Paños, Ramón Fuentes González (2001)

Mathware and Soft Computing

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Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature. In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implications),...

Rationality of induced ordered weighted operators based on the reliability of the source of information in group decision-making

Francisco Chiclana, Francisco Herrera, Enrique Herrera-Viedma (2004)

Kybernetika

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The aggregation of preference relations in group decision-making (GDM) problems can be carried out based on either the reliability of the preference values to be aggregated, as is the case with ordered weighted averaging operators, or on the reliability of the source of information that provided the preferences, as is the case with weighted mean operators. In this paper, we address the problem of aggregation based on the reliability of the source of information, with a double aim: a)...

Formal Introduction to Fuzzy Implications

Adam Grabowski (2017)

Formalized Mathematics

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In the article we present in the Mizar system the catalogue of nine basic fuzzy implications, used especially in the theory of fuzzy sets. This work is a continuation of the development of fuzzy sets in Mizar; it could be used to give a variety of more general operations, and also it could be a good starting point towards the formalization of fuzzy logic (together with t-norms and t-conorms, formalized previously).