Improvement of Proportional Conflict Redistribution Rules of Combination of Basic Belief Assignments
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This paper discusses and analyzes the behaviors of the Proportional Conflict Redistribution rules no. 5 (PCR5) and no. 6 (PCR6) to combine several distinct sources of evidence characterized by their basic belief assignments defined over the same frame of discernment. After a brief review of these rules, the paper shows through simple examples why their behaviors can sometimes increase the uncertainty more than necessary, which is detrimental to decision-making support drawn from the result of the combination. We present a theoretical improvement of these rules, and establish new PCR5+ and PCR6+ rules of combination. These new rules overcome the weakness of PCR5 and PCR6 rules by computing binary-keeping indexes that allow to keep only focal elements that play an effective role in the partial conflict redistribution. PCR5+ and PCR6+ rules are not associative but they preserve the neutrality of the vacuous belief assignment contrary to the PCR5 and PCR6 rules, and they make a more precise redistribution which does not increase improperly the mass of partial uncertainties.