Generalized belief function, plausibility function, and Dempster's combinational rule to fuzzy sets

Uncertainty always exists in nature and real systems. It is known that probability has been used traditionally in modeling uncertainty. Since a belief function was proposed as an another type of measuring uncertainty, Dempster-Shafer theory (DST) has been widely studied and applied in diverse areas. Because of the advent of computer technology, the representation of human knowledge can be processed by a computer in complex systems. The analysis of fuzzy data becomes increasingly important. Up to date, there are several generalizations of DST to fuzzy sets proposed in the literature. In this article, we propose another generalization of belief function, plausibility function, and Dempster’s combinational rule to fuzzy sets. We then make the comparisons of the proposed extension with some existing generalizations and show its effectiveness. © 2003 Wiley Periodicals, Inc.