An Improved Belief Entropy in Evidence Theory

Uncertainty measurement of the basic probability assignment function has always been a hot issue in Dempster-Shafer evidence. Many existing studies mainly consider the influence of the mass function itself and the size of the frame of discernment, so that the correlation between the subsets is ignored in the power set of the frame of discernment. Without making full use of the information contained in the evidence, the existing methods are less effective in some cases given in the paper. In this paper, inspired by Shannon entropy and Deng entropy, we propose an improved entropy that not only inherits the many advantages of Shannon entropy and Deng entropy, but also fully considers the relationship between subsets, which makes the improved entropy overcome the shortcomings of existing methods and have greater advantages in uncertainty measurement. Many numerical examples are used to demonstrate the validity and superiority of our proposed entropy in this paper.