Evidence combination for a large number of sources

TL;DR

This paper introduces the LNS combination rule, designed to effectively aggregate a large number of sources in belief function theory, especially when many sources are unreliable, by emphasizing commonalities among sources.

Contribution

A novel combination rule called LNS is proposed, capable of handling large numbers of sources with varying reliability, improving over existing methods in complexity and applicability.

Findings

LNS effectively combines many sources with reliability variation.

The rule maintains the spirit of conjunctive rule to reinforce agreement.

Experimental results confirm the rule's effectiveness on synthetic data.

Abstract

The theory of belief functions is an effective tool to deal with the multiple uncertain information. In recent years, many evidence combination rules have been proposed in this framework, such as the conjunctive rule, the cautious rule, the PCR (Proportional Conflict Redistribution) rules and so on. These rules can be adopted for different types of sources. However, most of these rules are not applicable when the number of sources is large. 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, named LNS (stands for Large Number of Sources), is proposed on the basis of a simple idea: the more common ideas one source shares with others, the morereliable the source is. This rule is adaptable for aggregating a large number of sources among which some are unreliable. 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. Moreover, it can be used to elicit the major opinion among the experts. The experimental results on synthetic mass functionsverify that the rule can be effectively used to combine a large number of mass functions and to elicit the major opinion.