Plausibility Entropy: A New Total Uncertainty Measure in Evidence Theory Based on Plausibility Function

Abstract

Evidence theory provides an effective representation and handling framework for uncertain information. However, the quantification for the uncertainty of mass function in this theory is still an unsolved problem. For two types of uncertainty involved in evidence theory, conflict, and nonspecificity, many measurement methods have been proposed on the basis of requirements of axiomatic conditions. However, these existing methods proposed to measure the uncertainty of mass function are of deficiencies more or less, such as low sensitivity, counter-intuition, dispute on maximum entropy, and so on. In order to overcome the above defects, a total uncertainty measure based on the plausibility function, named as plausibility entropy, is proposed in this article, which provides a new solution to measure the uncertainty of the mass function. By embodying the plausibility function and plausibility transformation of every singleton in the frame of discernment, the new measure enlarges the Shannon’s entropy of equivalent probability mass function obtained using the plausibility transformation, and establishes a quantitative relationship between uncertainty measure and Dempster’s rule of combination. Compared with existing uncertainty measures, the proposed plausibility entropy is more sensitive to changes in a mass function. It also satisfies many desirable axiomatic properties, including non-negativity, maximum entropy, probability consistency, monotonicity, and so on. Moreover, the relationship among axiomatic properties of uncertainty measures is also discussed in this article. Numerical examples and comparison are provided to illustrate the effectiveness and rationality of the proposed plausibility entropy.