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.
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.
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.
A modification of Dempster's and Pawlak's constructs forms a new foundation for the identification of upper and lower sets formulas. Also, in this modified Dempster-Pawlak construct we require that subsets of the power set be restricted to the well-known information granules of the power set. An aggregation of upper information granules amongst each other and lower information granules amongst each other determine upper and lower set formulas for both crisp and fuzzy sets. The results are equivalent...