An Improved Extension of the D-S Evidence Theory to Fuzzy Sets

To analyze fuzzy data in uncertain evidential reasoning, some researchers have recently extended the D-S evidence theory to fuzzy sets. But there are some insufficiencies in the definition of the fuzzy belief function and the combination rule on fuzzy sets of the D-S evidence theory. This paper describes a new definition of the similarity degree between two fuzzy sets and the improved extension combination rule of the evidence theory on fuzzy sets. It also presents the corresponding mathematical proof to validate the improved combination rule. Compared with other generalizing combination rules, the results of the numerical experiments show that the new combination rule in this paper can acquire more changing information to the change of fuzzy focal elements more effectively, and it overcomes the insufficiencies of other existing combination rules and enhances the robustness of fusion decision systems effectively.