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Dempster-Shafer theory (D-S theory) is widely used in decision making underthe uncertain environment. Ranking basic belief assignments (BBAs) now is anopen issue. Existing evidence distance measures cannot rank the BBAs in thesituations when the propositions have their own ranking order or their inherentmeasure of closeness. To address this issue, a new ranking evidence distance(RED) measure is proposed. Compared with the existing evidence distancemeasures including the Jousselme's distance and the distance between bettingcommitments, the proposed RED measure is much more general due to the fact thatthe order of the propositions in the systems is taken into consideration. Ifthere is no order or no inherent measure of closeness in the propositions, ourproposed RED measure is reduced to the existing evidence distance. Numericalexamples show that the proposed RED measure is an efficient alternative to rankBBAs in decision making under uncertain environment.

Ranking basic belief assignments in decision making under uncertain environment