Combination of sources of evidence with different discounting factors based on a new dissimilarity measure

The sources of evidence may have different reliability and importance in real applications for decision making. The estimation of the discounting (weighting) factors when the prior knowledge is unknown have been regularly studied until recently. In the past, the determination of the weighting factors focused only on reliability discounting rule and it was mainly dependent on the dissimilarity measure between basic belief assignments (bba's) represented by an evidential distance. Nevertheless, it is very difficult to characterize efficiently the dissimilarity only through an evidential distance. Thus, both a distance and a conflict coefficient based on probabilistic transformations BetP are proposed to characterize the dissimilarity. The distance represents the difference between bba's, whereas the conflict coefficient reveals the divergence degree of the hypotheses that two belief functions strongly support. These two aspects of dissimilarity are complementary in a certain sense, and their fusion is used as the dissimilarity measure. Then, a new estimation method of weighting factors is presented by using the proposed dissimilarity measure. In the evaluation of weight of a source, both its dissimilarity with other sources and their weighting factors are considered. The weighting factors can be applied in the both importance and reliability discounting rules, but the selection of the adapted discounting rule should depend on the actual application. Simple numerical examples are given to illustrate the interest of the proposed approach.

Research highlights
► The fusion of distance and conflict is proposed to measure dissimilarity of bba's.
► The distance and conflict are complementary in the evaluation of dissimilarity.
► All the weighting factors of sources are computed jointly by global optimization.
► Weighting factors are applied in importance (reliability) discounting rule.