Representations of synonymy and antonymy by automorphisms in fuzzy set theory.
Structures of automorphisms and automorphism groups in fuzzy set theory are studied in detail in view of applications to synonymy and antonymy representations.
Residual quotient fuzzy subset in near-rings.
Risk aversion, prudence and mixed optimal saving models
The paper studies risk aversion and prudence of an agent in the face of a risk situation with two parameters, one described by a fuzzy number, the other described by a fuzzy variable. The first contribution of the paper is the characterization of risk aversion and prudence in mixed models by conditions on the concavity and the convexity of the agent's utility function and its partial derivatives. The second contribution is the building of mixed models of optimal saving and their connection with...
Robust Rank Correlation Coefficients on the Basis of Fuzzy.
Rough relation properties
Rough Set Theory (RST) is a mathematical formalism for representing uncertainty that can be considered an extension of the classical set theory. It has been used in many different research areas, including those related to inductive machine learning and reduction of knowledge in knowledge-based systems. One important concept related to RST is that of a rough relation. This paper rewrites some properties of rough relations found in the literature, proving their validity.
-measures, -measures and distinguished classes of fuzzy measures
-measures are special fuzzy measures decomposable with respect to some fixed t-conorm . We investigate the relationship of -measures with some distinguished properties of fuzzy measures, such as subadditivity, submodularity, belief, etc. We show, for example, that each -measure is a plausibility measure, and that each -measure is submodular whenever is 1-Lipschitz.
Scalar cardinalities for divisors of a fuzzy cardinality.
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.
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
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.
Semigroup actions on intuitionistic fuzzy 2-metric spaces.
Semi-t-operators on a finite totally ordered set
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
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 -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.
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
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.
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
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
In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice based on a priori given t-norm acting on and t-conorm acting on for an arbitrary element . 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
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 -conjugate.
Some notes on U-partial order
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.
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.