The Information Volume of Uncertain Information: (5) Divergence Measure

Dempster-Shafer Evidence theory is an extension of probability theory, which can describe uncertain information more reasonably. Divergence measure is always an important concept in probability theory. Therefore, how to propose a reasonable divergence measurement has always been a research hot spot in evidence theory. Recently, Deng proposed the concept of information volume based on Deng entropy. It is interesting to note that compared with the uncertainty measure of Deng entropy, information volume of Deng entropy contains more information. Obviously, it might be more reasonable to use information volume of Deng entropy to represent uncertainty information. Based on this, in the paper, we combined the characteristics of non-specific measurement of Deng entropy, and propose a new divergence measure. The new divergence measurement not only satisfies the axiom of distance measurement, but also has some advantages that cannot be ignored. In addition, when the basic probability assignment(BPA) degenerates into probability distribution, the measured result of the new divergence measure is the same as that of the traditional Jensen-Shannon divergence. If the mass function is assigned in probability distribution, the proposed divergence is degenerated as Kullback-Leibler divergence. Finally, some numerical examples are illustrated to show the efficiency of the proposed divergence measure of information volume.