Generalization of Belief and Plausibility Functions to Fuzzy Sets Based on the Sugeno Integral

Uncertainty has been treated in science for several decades. It always exists in real systems. Probability has been traditionally used in modeling uncertainty. Belief and plausibility func-tions based on the Dempster–Shafer theory ~DST! become another method of measuring uncer-tainty, as they have been widely studied and applied in diverse areas. Conversely, a fuzzy set has been successfully used as the idea of partial memberships of multiple classes for the presenta-tion of unsharp boundaries. It is well used as the representation of human knowledge in complex systems. Nowadays, there exist several generalizations of belief and plausibility functions to fuzzy sets in the literature. In this article, we propose a new generalization of belief and plausi-bility functions to fuzzy sets based on the Sugeno integral. We then make comparisons of the proposed generalization with some existing methods. The results show the effectiveness of the proposed generalization, especially for being able to catch more information about the change of fuzzy focal elements. © 2007 Wiley Periodicals, Inc. 1