A novel divergence measure in Dempster–Shafer evidence theory based on pignistic probability transform and its application in multi-sensor data fusion

Abstract

Dempster–Shafer (D–S) evidence theory is more and more extensively applied in multi-sensor data fusion. However, it is still an open issue that how to effectively combine highly conflicting evidence in D–S evidence theory. In this article, a novel divergence measure, called pignistic probability transformation divergence, is proposed to measure the difference between evidences. The proposed pignistic probability transformation divergence can reflect the interaction between single-element and multi-element subsets by introducing the pignistic probability transformation, and satisfies the properties of boundedness, non-degeneracy, and symmetry. Moreover, the pignistic probability transformation divergence can degenerate as Jensen–Shannon divergence when mass function and the probability distribution are consistent. Based on the pignistic probability transformation divergence, a new multi-sensor data fusion method is presented. The proposed method takes advantage of pignistic probability transformation divergence to measure the discrepancy between evidences in order to obtain the credibility weights, and belief entropy to measure the uncertainty of the evidences in order to obtain the information volume weights, which can fully mine the potential information between evidences. Then, the credibility weights and the information volume weights are integrated to generate an appropriate weighted average evidence before using Dempster’s combination rule. The results of two application cases illustrate that the proposed method outperforms other related methods for combining highly conflicting evidences.