A new measure of dissimilarity between two basic belief assignments
Résumé
The measures of dissimilarity between basic belief assignments (bba's) in the framework of the theories of evidence have been regularly studied in the literature until recently. Nevertheless, the question is still open and it is very difficult to represent efficiently the dissimilarity between bba's through a single scalar measure. In this paper, we analyze the limitation of conflicting beliefs and the classical distance when they are used directly as dissimilarity measures. The main problem for evaluating the dissimilarity between two bba's lies in the relationship among their focal elements. Probabilistic transformations allow to approximate any bba into a subjective probability measure based on an underlying frame of discernment whose atomic elements are exhaustive and exclusive. In this paper, we propose to use both a distance based on probabilistic transformations (mainly the pignistic transformation BetP and the Dezert-Smarandache transformation DSmP) and also a conflict coefficient in order to charracterize and measure the dissimilarity between two bba's. Our approach takes into account both the difference between bba's (through the probabilistic distance) and the degree of divergence (through the conflict coefficient) of hypothesis that two belief functions strongly support. These two aspects of disimilarity are complementary in the evaluation of our dissimilarity measure. The method proposed in this paper is applied for evaluating the reliability of sources of evidence and selecting a rule of combination rule of bba's. Simple numerical examples are given to illustrate the interest of the proposed approach.
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