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S -measures, T -measures and distinguished classes of fuzzy measures

Peter Struk, Andrea Stupňanová (2006)

Kybernetika

S -measures are special fuzzy measures decomposable with respect to some fixed t-conorm S . We investigate the relationship of S -measures with some distinguished properties of fuzzy measures, such as subadditivity, submodularity, belief, etc. We show, for example, that each S P -measure is a plausibility measure, and that each S -measure is submodular whenever S is 1-Lipschitz.

Scalar cardinalities for divisors of a fuzzy cardinality.

Juan Casasnovas Casasnovas (2002)

Mathware and Soft Computing

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 set, A,...

Searching degrees of self-contradiction in Atanassov's fuzzy sets.

Elena E. Castiñeira, Susana Cubillo, Carmen Torres (2006)

Mathware and Soft Computing

In [11] and [12] Trillas et al. introduced the study of contradiction in the framework of Fuzzy Logic because of the significance to avoid contradictory outputs in the processes of inference. Later, the study of contradiction in the framework of intuitionistic or Atanassov s fuzzy sets was initiated in [6] and [5]. The aim of this work is to go into the problem of measuring the self-contradiction in the case of intuitionistc fuzzy sets, since it is interesting to know not only if a set is contradictory,...

Semicopulas: characterizations and applicability

Fabrizio Durante, José Quesada-Molina, Carlo Sempi (2006)

Kybernetika

We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.

Semi-t-operators on a finite totally ordered set

Yong Su, Hua-Wen Liu (2015)

Kybernetika

Recently, Drygaś generalized nullnorms and t-operators and introduced semi-t-operators by eliminating commutativity from the axiom of t-operators. This paper is devoted to the study of the discrete counterpart of semi-t-operators on a finite totally ordered set. A characterization of semi-t-operators on a finite totally ordered set is given. Moreover, The relations among nullnorms, t-operators, semi-t-operators and pseudo-t-operators (i. e., commutative semi-t-operators) on a finite totally ordered...

Several results on set-valued possibilistic distributions

Ivan Kramosil, Milan Daniel (2015)

Kybernetika

When proposing and processing uncertainty decision-making algorithms of various kinds and purposes, we more and more often meet probability distributions ascribing non-numerical uncertainty degrees to random events. The reason is that we have to process systems of uncertainties for which the classical conditions like σ -additivity or linear ordering of values are too restrictive to define sufficiently closely the nature of uncertainty we would like to specify and process. In cases of non-numerical...

Similarity in fuzzy reasoning.

Frank Klawonn, Juan Luis Castro (1995)

Mathware and Soft Computing

Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval as the basis...

Smooth implications on a finite chain

Yong Su (2019)

Kybernetika

Mas et al. adapted the notion of smoothness, introduced by Godo and Sierra, and discussed two kinds of smooth implications (a discrete counterpart of continuous fuzzy implications) on a finite chain. This work is devoted to exploring the formal relations between smoothness and other six properties of implications on a finite chain. As a byproduct, several classes of smooth implications on a finite chain are characterized.

Sobre funciones de negación en la teoría de conjuntos difusos.

Enric Trillas (1979)

Stochastica

En su trabajo de 1973, ya clásico, Bellman y Giertz probaron que P(X) es un retículo distributivo con máximo y mínimo sólo (con hipótesis muy razonables) bajo las usuales definiciones (A U B)(x) = máx {A(x),B(x)}, (A ∩ B)(x) = mín {A(x),B(x)}, tratando escasamente el formalismo analítico relativo a la negación. En el presente trabajo se prueba que tal P(X) es un álgebra de DeMorgan si y sólo si la función de negación posee generador aditivo y que tales negaciones constituyen, en un cierto grupo...

Some issues of fuzzy querying in relational databases

Miroslav Hudec, Miljan Vučetić (2015)

Kybernetika

Fuzzy logic has been used for flexible database querying for more than 30 years. This paper examines some of the issues of flexible querying which seem to have potential for further research and development from theoretical and practical points of view. More precisely, defining appropriate fuzzy sets for queries, calculating matching degrees for commutative and non-commutative query conditions, preferences, merging constraints and wishes, empty and overabundant answers, and views on practical realizations...

Some methods to obtain t-norms and t-conorms on bounded lattices

Gül Deniz Çaylı (2019)

Kybernetika

In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice L based on a priori given t-norm acting on [ a , 1 ] and t-conorm acting on [ 0 , a ] for an arbitrary element a L { 0 , 1 } . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.

Some notes on the category of fuzzy implications on bounded lattices

Amin Yousefi, Mashaallah Mashinchi, Radko Mesiar (2021)

Kybernetika

In this paper, we introduce the product, coproduct, equalizer and coequalizer notions on the category of fuzzy implications on a bounded lattice that results in the existence of the limit, pullback, colimit and pushout. Also isomorphism, monic and epic are introduced in this category. Then a subcategory of this category, called the skeleton, is studied. Where none of any two fuzzy implications are Φ -conjugate.

Some notes on U-partial order

M. Nesibe Kesicioğlu, Ü. Ertuğrul, F. Karaçal (2019)

Kybernetika

In this paper, an equivalence on the class of uninorms on a bounded lattice is discussed. Some relationships between the equivalence classes of uninorms and the equivalence classes of their underlying t-norms and t-conorms are presented. Also, a characterization for the sets admitting some incomparability w.r.t. the U-partial order is given.

Some properties concerning the quasi-inverse of a t-norm.

Dionís Boixader (1998)

Mathware and Soft Computing

Some properties of the quasi-inverse operators are presented. They are basic tools in order to reduce complex expressions involving several of such operators. An effective calculation for the quasi-inverse of a continuous t-norm is also provided.

Some properties of B -operations

Bohdan Butkiewicz (2007)

Kybernetika

In the paper the problem of mathematical properties of B -operations and weak W B -operations introduced by the author for interpretation of connectives “and”, “or”, and “also” in fuzzy rules is considered. In previous author’s papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system described by set of rules of the type if – then. Monotonicity condition, required for triangular norms, is...

Some results on the weak dominance relation between ordered weighted averaging operators and T-norms

Gang Li, Zhenbo Li, Jing Wang (2024)

Kybernetika

Aggregation operators have the important application in any fields where the fusion of information is processed. The dominance relation between two aggregation operators is linked to the fusion of fuzzy relations, indistinguishability operators and so on. In this paper, we deal with the weak dominance relation between two aggregation operators which is closely related with the dominance relation. Weak domination of isomorphic aggregation operators and ordinal sum of conjunctors is presented. More...

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