A New Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Belief Function and Plausibility Function

Abstract

How to measure the uncertainty of the basic probability assignment (BPA) function is an open issue in Dempster⁻Shafer (D⁻S) theory. The main work of this paper is to propose a new belief entropy, which is mainly used to measure the uncertainty of BPA. The proposed belief entropy is based on Deng entropy and probability interval consisting of lower and upper probabilities. In addition, under certain conditions, it can be transformed into Shannon entropy. Numerical examples are used to illustrate the efficiency of the new belief entropy in measurement uncertainty.

Keywords

• Dempster–Shafer (D–S) theory
• belief entropy
• Deng Entropy
• measurement uncertainty
• probability interval
• belief function