Conflict measure for the discounting operation on belief functions

Arnaud Martin B · Anne-Laure Jousselme · Christophe Osswald

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Multi-Criteria Decision Making Bayesian Modeling and Causal Inference Fuzzy and Soft Set Theory

Abstract

In the belief function theory, the concept of conflict appearing while confronting several expertspsila opinions can serve for many purposes, and in particular it can be used as an indicator of the relative reliability of the experts. The traditional definition of conflict as the basic belief assigned to the empty set during the combination has several issues and in particular it may not adequately represent the disagreement between the experts in presence. Hence, we propose some alternative measures of conflict as the distance between belief functions. These measures of conflict are further used for an a posteriori estimation of the relative reliability between the sources of information. This estimation of the reliability does not need any training or prior knowledge and can then be used to discount the unreliable sources before the combination step. These measures are evaluated and debated on random basic belief assignments and on real radar data.

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References

1987On the dempster-shafer framework and new combination rules 1990The combination of evidence in the transferable belief model 2000Combining belief functions when evidence conflicts 2001A new distance between two bodies of evidence 1988Representation and combination of uncertainty with belief functions and possibility measures 2004Combining belief functions based on distance of evidence 2002Belief function combination and conflict management 1990Constructing the Pignistic Probability Function in a Context of Uncertainty

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2010Conflict management in Dempster–Shafer theory using the degree of falsity 2010Fusion of sources of evidence with different importances and reliabilities 2016Belief Interval-Based Distance Measures in the Theory of Belief Functions 2013A proof for the positive definiteness of the Jaccard index matrix 2013How to preserve the conflict as an alarm in the combination of belief functions?2012

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