A representation theorem for probabilistic metric spaces in general
In this paper, we present a representation theorem for probabilistic metric spaces in general.
A short note on representation of L-fuzzy sets by Moore's families.
A stochastic model of choice.
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 supplement to Gottwald's note on fuzzy cardinals
A theorem for basis operators over intuitionistic fuzzy sets.
The concept of s-basis operators over intuitionistic fuzzy sets is introduced and all 2-, 3-, 4- basis operators are listed.
A theoretical comparison of disco and CADIAG-II-like systems for medical diagnoses
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 theoretical development of distance measure for intuitionistic fuzzy numbers.
A T-partial order obtained from T-norms
A partial order on a bounded lattice is called t-order if it is defined by means of the t-norm on . It is obtained that for a t-norm on a bounded lattice the relation iff for some 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 and a complete lattice on the subset of all elements of which are the supremum of a subset of atoms.
About the equivalence of nullnorms on bounded lattice
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.
Addition of fuzzy quantities: Disjunction-conjunction approach
Addition of rational fuzzy quantities: Convolutive approach
Aggregation operators and fuzzy measures on hypographs
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 and Lipschitzian Conditions.
Aggregation operators from the ancient NC and EM point of view
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
In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of -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
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...
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.