A generalized divergence of information volume and its applications. (February 2022) - Gao, Xiaozhuan; Pan, Lipeng; Deng, Yong
Abstract: Dempster–Shafer evidence theory provides a powerful method for the expression and fusion of uncertain information. When handling the high conflict information, traditional Dempster combination rule can produce counterintuitive results. Hence, the reasonable conflict measure is essential in information fusion. Inspired by this view, the paper propose the new method to measure conflict between bodies of evidence. Firstly, we define a new information volume of mass function for the perspective of information discord and non-specificity. Second, we propose a generalized divergence based on information volume of mass function, denoted as Jensen–Shannon divergence of information volume ( I J S ) . I J S can effectively measure the conflict between bodies of evidence. I J S reflects the conflict between bodies of evidence in terms of the differences between the support of propositions and the elements. That is, compared to the current approach, I J S not only fully considers the differences between the support degree of propositions, but also the differences of elements in propositions from the perspective of information non-specificity. When the mass function degenerates to a probabilistic distribution, I J S also degenerates to the classical Jensen–Shannon divergence. Meanwhile, I J S also satisfies the axioms of distance measure, such as non-negativity, symmetry and etc. Further, we proved these axioms based on mathematical derivation, and some numerical examples are applied to explain axioms and advantages. Based on the proposed divergence measure, we propose a multi-source information fusion method in the real world, and several data sets can be used to show that the proposed fusion method is superior to current method under the framework of evidence theory.