Plausibility Extropy: The Complementary Dual of Plausibility Entropy

Abstract

Measuring the uncertainty of information is a crucial problem in many fields. Recent studies have found a new uncertainty measure for probabilities called “extropy” as a complementary dual function of classical Shannon entropy. In this article, the extropy measure of randomness is generalized to the case of information with epistemic uncertainty by means of a framework of Dempster-Shafer evidence theory. Specifically, a novel measure called plausibility extropy is proposed, which inherits the intriguing properties of original extropy. Moreover, the duality and complementarity between the proposed plausibility extropy and existing plausibility entropy are proved strictly, which constitutes an entropy-extropy combination for mass functions to measure the epistemic uncertainty. In addition, the maximum plausibility extropy is also studied in this article. Through comparing with existing extropy-like measures in Dempster-Shafer evidence theory, the rationality of proposed plausibility extropy is further demonstrated.