Abstract
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.
Highlights
The theories of evidence [2,16,17,18], called theories of belief functions, are widely used in information fusion for decision making [3,8,14] as soon as the information to deal with are uncertain and possibly conflicting and represented by basic belief assignments
We have shown through simple examples that the notion of dissimilarity includes at least two aspects represented by the difference between bba's and by their level of conflict
A new conflict coefficient was introduced to overcome the limitations of the classical degree of conflict represented traditionally by the mass committed to the empty set through the conjunctive rule
Summary
The theories of evidence [2,16,17,18], called theories of belief functions, are widely used in information fusion for decision making [3,8,14] as soon as the information to deal with are uncertain and possibly conflicting and represented by basic belief assignments (bba's). The distance criterion measures the total difference between the bba's, whereas the conflict criterion reveals the degree of divergences between the distinct hypotheses strongly supported by each source. These two criteria are mutually compensable in a certain sense. The dB distance between m1 and m2 is larger than between m1 and m3 which is not a good behavior in authors opinions because m1 and m2 must be considered as quite similar since they represent a full uncertainty decision-making state From such a very simple example, one sees that dJ and dB are not well adapted to fully measure the dissimilarity between bba's
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