Fuzzy Approximation Operators Based on Coverings

Authors:
Tongjun Li;Jianmin Ma
Affiliations:
Mathematics, Physics and Information College, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, P.R. China and Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaoton ...;Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi, 710049, P.R. China
Venue:
RSFDGrC '07 Proceedings of the 11th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
Year:
2009

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Abstract

This paper presents a general framework for the study of covering-based fuzzy approximation operators in which a fuzzy set can be approximated by some elements in a crisp or a fuzzy covering of the universe of discourse. Two types of approximation operators, crisp-covering-based rough fuzzy approximation operators and fuzzy-covering-based fuzzy rough approximation operators, are defined, their properties are examined in detail. Finally, the comparison of these new approximation operators is done, a sufficient and necessary condition is given under which some operators are equivalent, and approximation operator characterization of fuzzy partitions of the universe is obtained.