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

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.

Quantifying leakage in the presence of unreliable sources of information

“…These metrics capture well the quality of the dissimilarity of opinions, that is, whether or not they distribute most of their support to compatible (viz same) elements. Having noticed that both approaches fail to give satisfactory results in general and that each of them capture only one of two complementary aspects of the dissimilarity, [59] propose to combine both approaches.…”

“…Recently, many discounting frameworks (e.g. [58,59]), mainly based on two di↵erent approaches, have been proposed to enhance the trustworthiness of information from unreliable sources of evidence. On the one hand, there are methods that propose distance metrics 8 to capture the level (viz the quantity) of the dissimilarity between di↵erent opinions, but cannot show whether or not they conflict in the hypothesis they strongly support.…”

“…The distance and conflict metrics of [59] translate in our setting as Dist(p, q) = 1 2 ⇣ X a2A |p(a) q(a)| ⌘ and Conf(p, q) = ⇢ 0 i fa r g m a x a2A p(a) \ argmax a2A q(a) 6 = ; p(a 0 )q(a 0 0 ) otherwise, where a 0 2 argmax a2A p(a) and a 0 0 2 argmax a2A q(a). An immediate consequence is that the distance between two beliefs is null if and only if the two opinions fully agree, i.e.…”

Adaptive imputation of missing values for incomplete pattern classification

“…BFT has already been applied successfully for object classification [20]- [28], clustering [29]- [33] and multi-source information fusion [34]- [37], etc. Some classifiers for the complete pattern based on DST have been developed by Denoeux and his collaborators to come up with the evidential K-nearest neighbors (EK-NN) [21], evidential neural network (ENN) [27], etc.…”

A New PCR Combination Rule for Dynamic Frame Fusion

“…In the dynamic frame fusion, frame of discernment changes with time taking in account the non-existential integrity constraints to establish new model of frame [3] . In the classical Dempster-Shafer theory (DS theory) [4−6] , the main research focus on the static fusion for nonexistence of non-existential integrity constraints concept, as computation problem [7] , static combination rule [8] , combination of unreliable evidence [9−11] , evidential classification method [12,13] . But the dynamic frame fusion is more practical than static fusion [14] .…”