Combination rule of D–S evidence theory based on the strategy of cross merging between evidences

Abstract

Recent studies on the combination rule of D–S evidence theory can be summarized as two categories, i.e. the methods based on modification for Dempster rule, and the methods based on correction to original evidence sources. However, both of them fail to deal with the role of cardinality of focal elements in process of combination, leading generally to the imperfect final results which are hard to show the inherent differences between different bodies of evidence. In this paper, we propose a combination rule based on the strategy of cross merging between evidences, a newly developed methodology which can better reflect the focusing degree of focal elements between bodies of evidence, and make final combination results more succinct, reasonable and valid. Throughout the process of combination, such global information as reliability, focusing weights, and expected support of evidences is thoroughly taken into account. In addition, an effort is made to allocate evidential conflict in proportion only among combination propositions in order to refine combination results and reduce their decision range. A numerical example and its modified version demonstrate that the presented approach has good adaptability to the evidences in accord or with high conflict, and significantly outperforms other combination methods of a similar kind.