Modeling Belief Propensity Degree: Measures of Evenness and Diversity of Belief Functions

Based on Klir’s framework of uncertainty, the total uncertainty (also called ambiguity) of belief function is linear addition of discord and nonspecificity. Though uncertainty measures of belief function have been discussed widely, there is no measure that can satisfy the monotonicity and range consistency properties at the same time. In this article, we discuss uncertainty measure of belief function from the perspective of information fractal dimension. An uncertainty quantity called evenness and its measure Eve are proposed, which can represent the belief propensity degree of belief function. We first propose the measures of diversity (normalized nonspecificity) and the element evenness (normalized discord), and then fuse them to calculate Eve. The proposed method can not only measure the subnormal mass function but also interpret the different views of Klir and Smets on “Uncertainty.” In addition, we extend Klir’s framework of uncertainty based on the proposed information quantities.