Approximation operators based on vague relations and roughness measures of vague sets

Abstract

Rough set theory and vague set theory are powerful tools for managing uncertain, incomplete and imprecise information. This paper extends the rough vague set model based on equivalence relations and the rough fuzzy set model based on fuzzy relations to vague sets. We mainly focus on the lower and upper approximation operators of vague sets based on vague relations, and investigate the basic properties of approximation operators on vague sets. Specially, we give some essential characterizations of the lower and upper approximation operators generated by reflexive, symmetric, and transitive vague relations. Finally, we structure a parameterized roughness measure of vague sets and similarity measure methods between two rough vague sets, and obtain some properties of the roughness measure and similarity measures. We also give some valuable counterexamples and point out some false properties of the roughness measure in the paper of Wang et al.

Keywords

vague relation / vague approximation space / rough vague set / roughness measure / similarity measure

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos.10341002, 60573063, and 60573064), the Natural Science Foundation of Guangdong (S2011010003681) , the Guangdong Science and Technology Plan Project (2010B010600039), the open foundation of Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences(No.IIP2010-5) and the Wuyi University key research foundation. The author is highly grateful to Professor Cungen Cao and reviewers for their suggestions for improving this paper.

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