Towards an efficient uncertainty measure of probability distribution set: From the belief structure perspective

Abstract

Bayesian probability theory models uncertainty of a random variable within an n-dimensional framework, employing n-dimensional weights. Shannon entropy, as a foundational concept in information theory, can effectively characterize the randomness of probability distribution. This paper will discuss an extended question: when multiple probability distributions jointly model a random variable, how can their uncertainty be characterized? In response to this issue, we considered a generalized expression of probability distribution - the belief structure to accomplish this task. By comparing with traditional entropy interval and the weighted average entropy approach, we demonstrate the rationality and effectiveness of the proposed method from both mathematical proof and practical application perspectives.