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

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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.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China

    Mingfen Wu

  2. School of Information Science, Wuyi University, Jiangmen, 529020, China

    Mingfen Wu

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  1. Mingfen Wu
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Correspondence to Mingfen Wu.

Additional information

Mingfen Wu received her BSc degree in mathematics from Nanjing Normal University in 1985, MSc degree in mathematics from Nanchang University in 1989. She is a visiting scholar of the Institute of Computing Technology, Chinese Academy of Sciences from 2008 to 2009. Now she is a professor of computer science in Wuyi University, a member of CCF and IACSIT. Her research interest focuses on fuzzy set theory, rough set theory and applications of these theories in data mining and artificial intelligence.

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Wu, M. Approximation operators based on vague relations and roughness measures of vague sets. Front. Comput. Sci. China 5, 429–441 (2011). https://doi.org/10.1007/s11704-011-9176-0

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