Affiliations: College of Science, Xi'an Shiyou University, Xi'an , 710065, China. [email protected] | College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China
Note: [] Address for correspondence: Xi'an Shiyou University, Xi'an 710065, China Supported by the S&T plan projects of Shaanxi Provincial Department of Education (No. 11JK0473) and the research funds of Xian Shiyou University for young scholars
Abstract: A propositional logic PRL for rough sets was proposed in [1]. In this paper, we initially introduce the concepts of rough (upper, lower) truth degrees on the set of formulas in PRL. Then, by grading the rough equality relations, we propose the concepts of rough (upper, lower) similarity degree. Finally, three different pseudo-metrics on the set of rough formulas are obtained, and thus an approximate reasoning mechanism is established.
