Title: Credibility measure of fuzzy sets and applications
Author: Xiang Li, Dan Ralescu
Department of Mathematics, Tsinghua University, Beijing 100084, China.
Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221, USA
Abstract: In order to measure a fuzzy event, credibility measure is proposed as a non-additive set function. In this paper, this concept is extended to fuzzy sets. First, a mean measure is defined by Lebesgue integral and some properties are investigated such as the monotonicity theorem, self-duality theorem and subadditivity theorem. Furthermore, by using Sugeno integral, an equilibrium measure is proposed and studied. Finally, these concepts are applied to optimisation problems, and the mean measure maximisation model and equilibrium measure maximisation model are proposed.
Keywords: fuzzy sets; credibility measure; Sugeno integral; optimisation; mean measure maximisation; equilibrium measure maximisation.
Int. J. of Advanced Intelligence Paradigms, 2009 Vol.1, No.3, pp.241 - 250
Available online: 19 Jun 2009