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Relations of granular worlds

Witold Pedrycz, George Vukovich (2002)

International Journal of Applied Mathematics and Computer Science

In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such it is very much oriented towards coping with the underlying it relational aspects of the experimental data. The second goal deals with a formation of a mapping between information granules constructed in two spaces (thus it concentrates on the it directional aspect of information...

Residual implications and co-implications from idempotent uninorms

Daniel Ruiz, Joan Torrens (2004)

Kybernetika

This paper is devoted to the study of implication (and co-implication) functions defined from idempotent uninorms. The expression of these implications, a list of their properties, as well as some particular cases are studied. It is also characterized when these implications satisfy some additional properties specially interesting in the framework of implication functions, like contrapositive symmetry and the exchange principle.

Resolución por programación paramétrica del problema multiobjetivo lineal difuso.

Miguel Delgado, José Luis Verdegay, Amparo Vila (1985)

Trabajos de Estadística e Investigación Operativa

En este artículo se propone una solución difusa al problema Multiobjetivo Lineal Difuso. Tal solución contiene, como valores particulares, las soluciones puntuales que otros autores han obtenido. El método que se emplea es independiente de las funciones de pertenencia que se consideren. El problema también se extiende al caso en que el conjunto de restricciones sea, junto con los objetivos, difuso.

Risk aversion, prudence and mixed optimal saving models

Irina Georgescu (2014)

Kybernetika

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...

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...

S-implications and R -implications on a finite chain

Margarita Mas, Miquel Monserrat, Joan Torrens (2004)

Kybernetika

This paper is devoted to the study of two kinds of implications on a finite chain L : S -implications and R -implications. A characterization of each kind of these operators is given and a lot of different implications on L are obtained, not only from smooth t-norms but also from non smooth ones. Some additional properties on these implications are studied specially in the smooth case. Finally, a class of non smooth t-norms including the nilpotent minimum is characterized. Any t-norm in this class...

Sobre el tamaño de muestra para experimentos aleatorios con imprecisión difusa.

M.ª Angeles Gil Alvarez, Pedro Gil Alvarez (1988)

Trabajos de Estadística

Statistical Inference deals with the drawing of conclusions about a random experiment on the basis of the information contained in a sample from it. A random experiment can be defined by means of the set of its possible outcomes (sample space) and the ability of observation of the experimenter. It is usually assumed that this ability allows the experimenter to describe the observable events as subsets of the sample space. In this paper, we will consider that the experimenter can only express the...

Some classes of divergence measures between fuzzy subsets and between fuzzy partitions.

Susana Montes, Pedro Gil (1998)

Mathware and Soft Computing

The aim of this paper is to present and study one important class of divergence measure between fuzzy subsets, and one important class of divergence measure between fuzzy partitions, each of them having some specific properties. In the first case, the divergence measure attempts to quantify the degree of difference between two fuzzy subsets ? and ? by comparing the fuzziness of both ? and ? with the fuzziness of the intermediate fuzzy subset. In the second case, we use this divergence between subsets...

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.

Specifying t-norms based on the value of T (1/2, 1/2).

Marcin Detyniecki, Ronald R. Yager, Bernadette Bouchon-Meunier (2000)

Mathware and Soft Computing

We study here the behavior of the t-norms at the point (1/2, 1/2). We indicate why this point can be considered as significant in the specification of t-norms. Then, we suggest that the image of this point can be used to classify the t-norms. We consider some usual examples. We also study the case of parameterized t-norms. Finally using the results of this study, we propose a uniform method of computing the parameters. This method allows not only having the same parameter-scale for all the families,...

Sur les mesures du degré de flou.

Enric Trillas, Claudi Alsina (1979)

Stochastica

On caractérise toutes les entropies-floues qui sont des valuations des treillis P(X) des parties floues d'un ensemble fini X, on presente la construction de certaines entropies floues et on analyse leur caractère de valuation de treillis aiguisés Sh(g), g belonging to P(X).

Symmetric implicational restriction method of fuzzy inference

Yiming Tang, Wenbin Wu, Youcheng Zhang, Witold Pedrycz, Fuji Ren, Jun Liu (2021)

Kybernetika

The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy...

T -extension as a method of construction of a generalized aggregation operator

Julija Lebedinska (2010)

Kybernetika

Generalized aggregation operators are the tool for aggregation of fuzzy sets. The apparatus was introduced by Takači in [11]. T -extension is a construction method of a generalized aggregation operator and we study it in the paper. We observe the behavior of a T -extension with respect to different order relations and we investigate properties of the construction.

Un algoritmo para construir codificaciones difusas balanceadas.

V. González de Garibay, L. Barba (1985)

Stochastica

Results assuring the existence of semilinear fuzzy partitions in 2, 3 or 4 balanced fuzzy classes are known. Such existence is not guaranteed for a greater number of classes. In this paper we present an algorithm that characterizes the set of solutions, and constructs any of them. Situations without a solution are also detected. We give a FORTRAN program for the algorithm and some examples.

Una medida de incertidumbre probabilística para sucesos difusos.

María Teresa López García, Pedro Gil Alvarez (1986)

Trabajos de Estadística

El objetivo de este artículo es proponer una medida de incertidumbre asociada a un conjunto difuso, de un referencial finito, que generalice la entropía de Shannon; es decir, que además de considerar la distribución de probabilidades definida en el referencial considere también la función de pertenencia del conjunto difuso.Posteriormente se estudian algunas propiedades de la medida propuesta.

Una nueva definición de aplicación difusa.

Miguel Delgado Calvo-Flores (1980)

Stochastica

If X, Y are universes of discourse, a fuzzy mapping f: X --> Y is defined as a classical mapping f: X x [0,1] --> P(Y). Their basic properties are studied as well as their relations with the classical model of fuzzy mapping.

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