Fuzzy Approximation Operators Based on Coverings

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.

[1]  Urszula Wybraniec-Skardowska,et al.  Extensions and Intentions in the Ruogh Set Theory , 1998, Inf. Sci..

[2]  Tong-Jun Li.  Rough Approximation Operators in Covering Approximation Spaces , 2006, RSCTC.

[3]  Yiyu Yao,et al.  Constructive and Algebraic Methods of the Theory of Rough Sets , 1998, Inf. Sci..

[4]  Wei-Zhi Wu,et al.  Constructive and axiomatic approaches of fuzzy approximation operators , 2004, Inf. Sci..

[5]  Yiyu Yao,et al.  Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators , 1998, Inf. Sci..

[6]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.

[7]  Nehad N. Morsi,et al.  Axiomatics for fuzzy rough sets , 1998, Fuzzy Sets Syst..

[8]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[9]  J. A. Pomykala,et al.  On definability in the nondeterministic information system , 1988 .

[10]  Wen-Xiu Zhang,et al.  An axiomatic characterization of a fuzzy generalization of rough sets , 2004, Inf. Sci..

[11]  W. Zakowski.  APPROXIMATIONS IN THE SPACE (U,π) , 1983 .

[12]  Wei-Zhi Wu,et al.  Neighborhood operator systems and approximations , 2002, Inf. Sci..

[13]  Chris Cornelis,et al.  Fuzzy rough sets: beyond the obvious , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[14]  Yiyu Yao,et al.  Rough sets, neighborhood systems and granular computing , 1999, Engineering Solutions for the Next Millennium. 1999 IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.99TH8411).

[15]  Sudarsan Nanda,et al.  Fuzziness in rough sets , 2000, Fuzzy Sets Syst..

[16]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[17]  Daniel Vanderpooten,et al.  A Generalized Definition of Rough Approximations Based on Similarity , 2000, IEEE Trans. Knowl. Data Eng..

[18]  Wei-Zhi Wu,et al.  Covering-Based Generalized Rough Fuzzy Sets , 2006, RSKT.