Ranking basic belief assignments in decision making under uncertain environment
This addresses an open issue in uncertain decision-making for applications like information fusion or risk assessment, but it is incremental as it extends existing distance measures.
The paper tackles the problem of ranking basic belief assignments (BBAs) in Dempster-Shafer theory for decision-making under uncertainty, where existing distance measures fail when propositions have inherent order or closeness. It proposes a new ranking evidence distance (RED) measure that incorporates proposition order, showing it is more general and efficient through numerical examples.
Dempster-Shafer theory (D-S theory) is widely used in decision making under the uncertain environment. Ranking basic belief assignments (BBAs) now is an open issue. Existing evidence distance measures cannot rank the BBAs in the situations when the propositions have their own ranking order or their inherent measure of closeness. To address this issue, a new ranking evidence distance (RED) measure is proposed. Compared with the existing evidence distance measures including the Jousselme's distance and the distance between betting commitments, the proposed RED measure is much more general due to the fact that the order of the propositions in the systems is taken into consideration. If there is no order or no inherent measure of closeness in the propositions, our proposed RED measure is reduced to the existing evidence distance. Numerical examples show that the proposed RED measure is an efficient alternative to rank BBAs in decision making under uncertain environment.