To avoid counter-intuitive result of classical Dempster's combination rule when dealing with highly conflict information, many improved combination methods have been developed through modifying the basic probability assignments (BPAs) of bodies of evidence (BOEs) by using a certain measure of the degree of conflict or uncertain information, such as Jousselme's distance, the pignistic probability distance and the ambiguity measure. However, if BOEs contain some non-singleton elements and the differences among their BPAs are larger than 0.5, the current conflict measure methods have limitations in describing the interrelationship among the conflict BOEs and may even lead to wrong combination results. In order to solve this problem, a new distance function, which is called supporting probability distance, is proposed to characterize the differences among BOEs. With the new distance, the information of how much a focal element is supported by the other focal elements in BOEs can be given. Also, a new combination rule based on the supporting probability distance is proposed for the combination of the conflicting evidences. The credibility and the discounting factor of each BOE are generated by the supporting probability distance and the weighted BOEs are combined directly using Dempster's rules. Analytical results of numerical examples show that the new distance has a better capability of describing the interrelationships among BOEs, especially for the highly conflicting BOEs containing non-singleton elements and the proposed new combination method has better applicability and effectiveness compared with the existing methods.
Bibliographical noteFunding: National Natural Science Foundation of China (Nos. 50905013 and 51211130114), the Royal Society International Exchange Grant of United Kingdom (No. IE111065), the Fundamental Research Funds for the Central Universities special funds of China (No. FRF-TP-09-014A), and Beijing Higher Education Young Elite Teacher Project of China (No. YETP0364)
- evidence conflict
- evidence theory
- information fusion
- Pignistic probability function
- supporting probability function