A Belief Combination Rule for a Large Number of Sources

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1 June 2019
Kuang Zhou, Arnaud Martin, Quan Pan

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The theory of belief functions is widely used for data from multiple sources. Different evidence combination rules have been proposed in this framework according to the properties of the sources to combine. However, most of these combination rules are not efficient when there are a large number of sources. This is due to either the complexity or the existence of an absorbing element such as the total conflict mass function for the conjunctive based rules when applied on unreliable evidence. In this paper, based on the assumption that the majority of sources are reliable, a combination rule for a large number of sources is proposed using a simple idea: the more common ideas the sources share, the more reliable these sources are supposed to be. This rule is adaptable for aggregating a large number of sources which may not all be reliable. It will keep the spirit of the conjunctive rule to reinforce the belief on the focal elements with which the sources are in agreement. The mass on the empty set will be kept as an indicator of the conflict.

The proposed rule, called LNS-CR (Conjunctive combination Rule for a Large Number of Sources), is evaluated on synthetic mass functions. The experimental results verify that the rule can be effectively used to combine a large number of mass functions and to elicit the major opinion.