Abstract
This is a study of fuzzy measures and fuzzy inte-grals; it presents some of the phenomena wherethey are used. It exposes how the concept of fuzzymeasure is introduced and from it, the notion offuzzy integral is presented. Properties of fuzzymeasures are established and they are classifiedaccording to additive property and λ-measures,while the probability, plausibility, credibility, pos-sibility and necessity measures are observed asclassic examples of the classification completed.The two main fuzzy integrals were analyzed: theSugeno integral and the Choquet integral, giventhe application of these integrals is made on finitesets, a comparison between them for the finitecase is performed using the concept of equiorde-red functions. We present two examples in whichfuzzy measures and fuzzy integrals are used inthe classification of individuals and in qualityassessment. It also describes some phenomenawhere they are applied. Classic measures are usedin certain special cases of uncertainty based onrandomness. The use in certain contexts of fuzzymeasures (non-additive) and fuzzy integrals offera more flexible and realistic focus in modelinguncertainty
Highlights
We present two examples in which fuzzy measures and fuzzy integrals are used in the classification of individuals and in quality assessment
Journal of Mathematical Analysis and Applications 101:114-138 Zadeh LA (1965) Fuzzy sets
Summary
Se hace un análisis de las dos principales integrales difusas: integral de Sugeno e integral de Choquet, dado que la aplicación de estas integrales se hace sobre conjuntos finitos, se realiza utilizando el concepto de función equiordenada una comparación de ellas para el caso finito. Una de las características principales de las medidas difusas es que no requieren la propiedad de la aditividad, en contraste con las medidas clásicas; por eso también son llamadas medidas no aditivas. Wang (1984, 1985) introduce algunos conceptos nuevos sobre las características estructurales de las medidas difusas, y por medio de ellos genera un desarrollo de la teoría general de las medidas difusas: nulaaditividad, autocontinuidad, autocontinuidad uniforme, pseudo nulaaditividad y pseudo autocontinuidad, entre otras. El propósito de este trabajo es realizar un estudio de las medidas difusas y las integrales difusas, incluyendo principalmente sus propiedades, clasificaciones, ejemplos y propiedades estructurales
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