Research on the combination rules of the D-S evidence theory and improvement of extension to fuzzy sets

As a popular information fusion method and easy to be combined with other intelligent methods, the Dempster-Shafter (D-S) Evidence Theory is more widely usable and can be extended very well in the future. For dealing with the deficiency of the evidence conflict, the combination rules of the D-S Evidence Theory are improved considering both coherent and incoherent information obtained from multiple sources. The corresponding experiments and theoretical analysis validate the improved rules can process both highly conflicting and coherent evidence effectively, and reasonable results with better convergence efficiency are given than other rules in the case of highly conflicting evidence sources. To analyze fuzzy data in uncertain evidential reasoning, the D-S evidence theory was extended to fuzzy sets. This paper describes a new definition of the similarity degree between two fuzzy sets and the improved extension combination rules of the evidence theory on fuzzy sets. 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.