Uncertainty Measure of Basic Probability Assignment Based on Renyi Entropy and Its Application in Decision-Making

Since the Dempster-Shafer evidence theory was developed, it has been extensively concerned by researchers. Compared with Bayesian probability theory, Dempster-Shafer evidence theory satisfies weaker constraints and has the advantage to indicate uncertainty, so it is widely used in the information system. However, how to measure the uncertainty of basic probability assignment in Dempster-Shafer evidence theory is still a problem worthy of attention. Therefore, based on Renyi entropy, this paper proposes a novel method to measure the uncertainty of basic probability assignment in Dempster-Shafer evidence theory. In addition, after proving that this method is compatible with Shannon entropy, a large number of comparative experiments are carried out to illustrate its effectiveness. Finally, through the application in decision-making, it is proved that the combination rule considering uncertainty can produce more reasonable results.