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A principal topology obtained from uninorms

Funda Karaçal, Tuncay Köroğlu (2022)

Kybernetika

We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice...

A reflection on what is a membership function.

Enric Trillas, Claudi Alsina (1999)

Mathware and Soft Computing

This paper is just a first approach to the idea that the membership function μP of a fuzzy set labelled P is, basically, a measure on the set of linguistic expressions x is P for each x in the corresponding universe of discourse X. Estimating that the meaning of P (relatively to X) is nothing else than the use of P on X, these measures seem to be reached by generalizing to a preordered set the concept of Fuzzy Measure, introduced by M. Sugeno, when the preorder translates the primary use of the...

A stochastic model of choice.

Sergei V. Ovchinnikov (1985)

Stochastica

An approach to choice function theory is suggested which is probabilistic and non-deterministic. In the framework of this approach fuzzy choice functions are introduced and a number of necessary and sufficient conditions for a fuzzy choice function to be a fuzzy rational choice function of a certain type are established.

A theoretical comparison of disco and CADIAG-II-like systems for medical diagnoses

Tatiana Kiseliova (2006)

Kybernetika

In this paper a fuzzy relation-based framework is shown to be suitable to describe not only knowledge-based medical systems, explicitly using fuzzy approaches, but other ways of knowledge representation and processing. A particular example, the practically tested medical expert system Disco, is investigated from this point of view. The system is described in the fuzzy relation-based framework and compared with CADIAG-II-like systems that are a “pattern” for computer-assisted diagnosis systems based...

A T-partial order obtained from T-norms

Funda Karaçal, M. Nesibe Kesicioğlu (2011)

Kybernetika

A partial order on a bounded lattice L is called t-order if it is defined by means of the t-norm on L . It is obtained that for a t-norm on a bounded lattice L the relation a ⪯ T b iff a = T ( x , b ) for some x ∈ L is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of L and a complete lattice on the subset A of all elements of L which are the supremum of a subset of atoms.

About the equivalence of nullnorms on bounded lattice

M. Nesibe Kesicioğlu (2017)

Kybernetika

In this paper, an equivalence on the class of nullnorms on a bounded lattice based on the equality of the orders induced by nullnorms is introduced. The set of all incomparable elements w.r.t. the order induced by nullnorms is investigated. Finally, the recently posed open problems have been solved.

Aggregation operators and fuzzy measures on hypographs

Doretta Vivona, Maria Divari (2002)

Kybernetika

In a fuzzy measure space we study aggregation operators by means of the hypographs of the measurable functions. We extend the fuzzy measures associated to these operators to more general fuzzy measures and we study their properties.

Aggregation operators from the ancient NC and EM point of view

Ana Pradera, Enric Trillas (2006)

Kybernetika

This paper deals with the satisfaction of the well-known Non-Contradiction (NC) and Excluded-Middle (EM) principles within the framework of aggregation operators. Both principles are interpreted in a non-standard way, based on self-contradiction (as in Ancient Logic) instead of falsity (as in Modern Logic). The logical negation is represented by means of strong negation functions, and conditions are given both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given...

Aggregation operators on partially ordered sets and their categorical foundations

Mustafa Demirci (2006)

Kybernetika

In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of L -fuzzy set-theoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furthermore, we will show that there exists a strong connection between the category of aggregation operators...

Aggregations preserving classes of fuzzy relations

Józef Drewniak, Urszula Dudziak (2005)

Kybernetika

We consider aggregations of fuzzy relations using means in [0,1] (especially: minimum, maximum and quasilinear mean). After recalling fundamental properties of fuzzy relations we examine means, which preserve reflexivity, symmetry, connectedness and transitivity of fuzzy relations. Conversely, some properties of aggregated relations can be inferred from properties of aggregation results. Results of the paper are completed by suitable examples and counter- examples, which is summarized in a special...

Algebras difusas.

Javier Montero de Juan (1985)

Trabajos de Estadística e Investigación Operativa

En este trabajo se propone una estructura de álgebra difusa (borrosa) basada en la distinción entre difusidad extensiva y comprehensiva, desarrollando y conectando los trabajos de Nahmias sobre variables difusas, de Klement sobre medibilidad difusa y de Nowakowska sobre estructuras de conceptos.

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