Algebraic equivalences over fuzzy quantities
Algebras difusas.
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.
Alternative model of fuzzy NTU coalitional game
One of the possible models of fuzzification of non-transferable utility (NTU) coalitional games was extensively treated in [4]. In this paper, we suggest an alternative structure of fuzzification of the NTU games, where for every coalition a fuzzy class of (generally crisp) sets of its admissible pay-off vectors is considered. It is shown that this model of a fuzzy coalitional game can be represented by a fuzzy class of deterministic NTU games, and its basic concepts like the superadditivity or...
An additive decomposition of fuzzy numbers
Hong and Do[4] improved Mareš[7] result about additive decomposition of fuzzy quantities concerning an equivalence relation. But there still exists an open question which is the limitation to fuzzy quantities on R (the set of real numbers) with bounded supports in the presented theory. In this paper we restrict ourselves to fuzzy numbers, which are fuzzy quantities of the real line R with convex, normalized and upper semicontinuous membership function and prove this open question.
An algorithm of calculation of lower solutions of fuzzy relational equations.
This paper deals with the problem of the determination of lower solutions of fuzzy relational equations. An algorithm of calculation of such a solution is presented.
An Algorithm to Compute theTransitive Closure, a Transitive Approximation and a Transitive Opening of a Fuzzy Proximity.
An alternative approach to rough sets
An Approach for Selecting Appropriate Methods for Treating Uncertainty in Knowledge Based Systems
An architecture for making judgments using computing with words
Our thesis is that computing with words needs to account for the uncertainties associated with the meanings of words, and that these uncertainties require using type-2 fuzzy sets. Doing this leads to a proposed architecture for making it judgments by means of computing with words, i.e., to a perceptual computer-the Per-C. The Per-C includes an encoder, a type-2 rule-based fuzzy logic system, and a decoder. It lets all human-computer interactions be performed using words. In this paper, a quantitative...
An axiomatization of fuzzy classes.
An axiomatization of fuzzy classes more general than usual fuzzy sets is proposed. Connections and interpretations with other axiomatizations of set theory and fuzzy set theory are investigated.
An extension method for t-norms on subintervals to t-norms on bounded lattices
In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on from the t-norm on a subinterval of need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction...
An extension of the ordering based on nullnorms
In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the -partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms.
An individual ergodic theorem for random fuzzy sets.
Analyse hiérarchique des préférences et généralisations de la transitivité
Approximations of lattice-valued possibilistic measures
Lattice-valued possibilistic measures, conceived and developed in more detail by G. De Cooman in 1997 [2], enabled to apply the main ideas on which the real-valued possibilistic measures are founded also to the situations often occurring in the real world around, when the degrees of possibility, ascribed to various events charged by uncertainty, are comparable only quantitatively by the relations like “greater than” or “not smaller than”, including the particular cases when such degrees are not...
Assignment problem with fuzzy estimates of effectiveness
Associative -dimensional copulas
The associativity of -dimensional copulas in the sense of Post is studied. These copulas are shown to be just -ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.
Axiomatizability in fuzzy logic
Bell-type inequalities for parametric families of triangular norms
In recent work we have shown that the reformulation of the classical Bell inequalities into the context of fuzzy probability calculus leads to related inequalities on the commutative conjunctor used for modelling pointwise fuzzy set intersection. Also, an important role has been attributed to commutative quasi-copulas. In this paper, we consider these new Bell-type inequalities for continuous t-norms. Our contribution is twofold: first, we prove that ordinal sums preserve these Bell-type inequalities;...
Binary Relations-based Rough Sets – an Automated Approach
Rough sets, developed by Zdzisław Pawlak [12], are an important tool to describe the state of incomplete or partially unknown information. In this article, which is essentially the continuation of [8], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library [11]). Here we drop the classical equivalence- and tolerance-based models of rough...