In this paper, the concepts of -fuzzy -open sets and -fuzzy basically disconnected spaces are introduced in the sense of Šostak and Ramadan. Some interesting properties and characterizations are studied. Tietze extension theorem for -fuzzy basically disconnected spaces is discussed.
Probability on collections of fuzzy sets can be developed as a generalization of the classical probability on -algebras of sets. A Łukasiewicz tribe is a collection of fuzzy sets which is closed under the standard fuzzy complementation and under the pointwise application of the Łukasiewicz t-norm to countably many fuzzy sets. An observable is a fuzzy set-valued mapping defined on a -algebra of sets and satisfying some additional properties; formally, the role of an observable is in a sense analogous...
After recalling the axiomatic concept of fuzziness measure, we define some fuzziness measures through Sugeno's and Choquet's integral. In particular, for the so-called homogeneous fuzziness measures we prove two representation theorems by means of the above integrals.
En este trabajo se realiza un estudio de Medidas de Nitidez para conjuntos difusos. Se comienza dando los conceptos de Medida Puntual de Nitidez o Auto-nitidez puntual y Medida de Nitidez para conjunto difuso, pasando a continuación a dar dos teoremas de construcción de Medidas de Nitidez y uno de caracterización para aquellas medidas que sean valoraciones en el retículo Ln(X).
This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to fuzzy relational equations and an inequality constraint, where is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy relational equation and an inequality constraint,...
This paper considers compositions of relations based on the notion of the afterset and the foreset, i. e., the subproduct, the superproduct and the square product introduced by Bandler and Kohout with modification proposed by De Baets and Kerre. There are proven all possible mixed pseudo-associativity properties of Bandler – Kohout compositions of relations.
Standard Möbius transform evaluation formula for the Choquet integral is associated with the -aggregation. However, several other aggregation operators replacing operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method...
En este artículo se considera un programa de Programación Lineal en el que los coeficientes del sistema de inecuaciones lineales, que definen el conjunto de restricciones, están dados de forma imprecisa o vaga. Se supone entonces que tales coeficientes pueden ser definidos mediante números difusos. Se propone un enfoque de resolución basado en las distintas versiones existentes para la comparación de números difusos. Finalmente, se obtienen diferentes modelos auxiliares de Programación Lineal, que...