Affiliations: [a] College of Computer, Minnan Normal University, Zhang’zhou, Fu’jian, China
| [b] School of Mathematics and Statistics, Minnan Normal University, Zhang’zhou, Fu’jian, China
| [c] Key Laboratory of Data Science and Intelligence Application, Fujian Province University, Zhangzhou, China
| [d] Key Laboratory of Granular Computing, Minnan Normal University, Zhangzhou, China
Abstract: The rough set theory and the evidence theory are two important methods used to deal with uncertainty. The relationships between the rough set theory and the evidence theory have been discussed. In covering rough set theory, several pairs of covering approximation operators are characterized by belief and plausibility functions. The purpose of this paper is to review and examine interpretations of belief functions in covering approximation operators. Firstly, properties of the belief structures induced by two pairs of covering approximation operators are presented. Then, for a belief structure with the properties, there exists a probability space with a covering such that the belief and plausibility functions defined by the given belief structure are, respectively, the belief and plausibility functions induced by one of the two pairs of covering approximation operators. Moreover, two necessary and sufficient conditions for a belief structure to be the belief structure induced by one of the two pairs of covering approximation operators are presented.
Keywords: Belief and plausibility functions, Covering approximation operators, Covering rough set, Evidence theory
