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

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.

Conflict Management for Target Recognition Based on PPT Entropy and Entropy Distance

Conflicting evidence affects the final target recognition results. Thus, managing conflicting evidence efficiently can help to improve the belief degree of the true target. In current research, the existing approaches based on belief entropy use belief entropy itself to measure evidence conflict. However, it is not convincing to characterize the evidence conflict only through belief entropy itself. To solve this problem, we comprehensively consider the influences of the belief entropy itself and mutual belief entropy on conflict measurement, and propose a novel approach based on an improved belief entropy and entropy distance. The improved belief entropy based on pignistic probability transformation function is named pignistic probability transformation (PPT) entropy that measures the conflict between evidences from the perspective of self-belief entropy. Compared with the state-of-the-art belief entropy, it can measure the uncertainty of evidence more accurately, and make full use of the intersection information of evidence to estimate the degree of evidence conflict more reasonably. Entropy distance is a new distance measurement method and is used to measure the conflict between evidences from the perspective of mutual belief entropy. Two measures are mutually complementary in a sense. The results of numerical examples and target recognition applications demonstrate that our proposed approach has a faster convergence speed, and a higher belief degree of the true target compared with the existing methods.

Discrete Arrow–Pratt indexes for risk and uncertainty

The Arrow–Pratt index, a gold standard in studies of risk attitudes, is not directly observable from choice data. Existing methods to measure it rely on parametric assumptions. We introduce a discrete Arrow–Pratt index, and its relative counterpart, that can be directly obtained from choices. Our approach is general: it is (i) non-parametric, (ii) applicable to both risk and uncertainty, (iii) and robust to probability transformation, non-additive beliefs and multiple priors. Our index can also be used to characterize various decision models through various simple consistency requirements. We analyze its properties and demonstrate how it can be measured.