A generalized belief dissimilarity measure based on weighted conflict belief and distance metric and its application in multi-source data fusion

Abstract

Dissimilarity measure between basic probability assignments (BPAs) in the Dempster-Shafer evidence structure is a vibrant research topic in artificial intelligence. However, there are flaws in the existing measurements. In particular, it is insufficient to characterize dissimilarity only from either evidential distance or conflict belief for a BPA. As such, we propose a new dissimilarity measure which takes into consideration both distance measure and conflict belief among betting commitments. These two factors complement with each other. Distance measure reflects diversity between the focal elements of two pieces of evidence. That is to say, the more intersections between the bodies of evidence (BOE) of two data sources, the more reliable it acts as a dissimilarity measure. Conversely, the conflict belief which is created based on the transformed Pignistic probability characterizes the product of singleton's belief from two pieces of evidence whose intersection is empty. It quantifies dissimilarity measure more efficiently when the focal elements of two pieces of evidence have small intersect. Theoretically, the new dissimilarity measure satisfies reflexivity, symmetry, nonnegativity, nondegeneracy and some other properties. Comparative analysis is provided with some cases to demonstrate the applicability and validity of the proposed dissimilarity measure. To determine the weight and reliability of evidence, the new dissimilarity measure among evidence and uncertainty of BPA are used. The dissimilarity metric is further applied for multi-source data fusion together with uncertainty measure of belief structure. The application of large-scale group decision making (LSGDM) problem is given to illustrate the effectiveness of the proposed multi-source data fusion process.