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

Lipeng Pan; Yong Deng

doi:10.3390/e20110842

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

Entropy (Basel). 2018 Nov 3;20(11):842. doi: 10.3390/e20110842.

Authors

Lipeng Pan¹, Yong Deng¹

Affiliation

¹ Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, China.

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; Deng Entropy; belief entropy; belief function; measurement uncertainty; probability interval.

Grants and funding

61573290, 61503237/National Natural Science Foundation of China