Generalized fuzzy rough sets. (English) Zbl 1019.03037

Summary: This paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper generalized approximation operators is defined. The connections between fuzzy relations and fuzzy rough approximation operators are examined. In the axiomatic approach, various classes of fuzzy rough approximation operators are characterized by different sets of axioms. Axioms of fuzzy approximation operators guarantee the existence of certain types of fuzzy relations producing the same operators.


03E72 Theory of fuzzy sets, etc.
Full Text: DOI


[1] Bodjanova, S., Approximation of a fuzzy concepts in decision making, Fuzzy sets and systems, 85, 23-29, (1997) · Zbl 0907.90003
[2] Chakrabarty, K.; Biswas, R.; Nanda, S., Fuzziness in rough sets, Fuzzy sets and systems, 110, 247-251, (2000) · Zbl 0943.03040
[3] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, International journal of general systems, 17, 191-208, (1990) · Zbl 0715.04006
[4] Dubois, D.; Prade, H., Twofold fuzzy sets and rough sets–some issues in knowledge representation, Fuzzy sets and systems, 23, 3-18, (1987) · Zbl 0633.68099
[5] Jagielska, I.; Matthews, C.; Whitfort, T., An investigation into the application of neural networks, fuzzy logic, genetic algorithms, and rough sets to automated knowledge acquisition for classification problems, Neurocomputing, 24, 37-54, (1999) · Zbl 0922.68096
[6] Kryszkiewicz, M., Rough set approach to incomplete information systems, Information sciences, 112, 39-49, (1998) · Zbl 0951.68548
[7] Kuncheva, L.I., Fuzzy rough sets: application to feature selection, Fuzzy sets and systems, 51, 147-153, (1992)
[8] T.Y. Lin, Neighborhood systems and relational database, Proceeding of CSC’88, 1988
[9] T.Y. Lin, Neighborhood systems–application to qualitative fuzzy and rough sets, in: P.P. Wang (Ed.), Advances in Machine Intelligence and Soft-Computing, Department of Electrical Engineering, Duke University, Durham, NC, USA, 1997, pp. 132-155
[10] Lin, T.Y.; Liu, Q., Rough approximate operators: axiomatic rough set theory, (), 256-260 · Zbl 0818.03028
[11] T.Y. Lin, Q. Lin, K.J. Huang, W. Chen, Rough sets, neighborhood systems and application, in: Z.W. Ras, M. Zemankova, M.L. Emrichm (Eds.), Methodologies for Intelligent Systems, Proceedings of the Fifth International Symposium on Methodologies of Intelligent Systems, Knoxville, Tennessee, 25-27 October 1990, North-Holland, New York, pp. 130-141
[12] T.Y. Lin, Y. Y. Yao, Mining soft rules using rough sets and neighborhoods, in: Proceedings of the Symposium on Modelling, Analysis and Simulation, Computational Engineering in Systems Applications (CESA’96), IMASCS Multiconference, Lille, France, 9-12 July 1996, pp. 1095-1100
[13] Morsi, N.N.; Yakout, M.M., Axiomatics for fuzzy rough sets, Fuzzy sets and systems, 100, 327-342, (1998) · Zbl 0938.03085
[14] Nakamura, A.; Gao, J.M., On a KTB-modal fuzzy logic, Fuzzy sets and systems, 45, 327-334, (1992) · Zbl 0754.03014
[15] Nanda, S.; Majumda, S., Fuzzy rough sets, Fuzzy sets and systems, 45, 157-160, (1992) · Zbl 0749.04004
[16] Nguyen, H.T., Some mathematical structures for computational information, Information sciences, 128, 67-89, (2000) · Zbl 0971.68161
[17] Pal, S.K., Roughness of a fuzzy set, Information sciences, 93, 235-246, (1996) · Zbl 0879.04004
[18] Pawlak, Z., Rough sets, International journal of computer and information science, 11, 341-356, (1982) · Zbl 0501.68053
[19] Pawlak, Z., Rough sets: theoretical aspects of reasoning about data, (1991), Kluwer Academic Publishers Boston · Zbl 0758.68054
[20] Pomykala, J.A., Approximation operations in approximation space, Bulletin of the Polish Academy of sciences: mathematics, 35, 653-662, (1987) · Zbl 0642.54002
[21] Quafafou, M., α-RST: a generalization of rough set theory, Information sciences, 124, 301-316, (2000) · Zbl 0957.68114
[22] R. Slowinski, D. Vanderpooten, Similarity relation as a basis for rough approximations, in: P.P. Wang (Ed.), Advances in Machine Intelligence and Soft-Computing, Department of Electrical Engineering, Duke University, Durham, NC. USA, 1997, pp. 17-33
[23] Tsumoto, S., Automated extraction of medical expert system rules from clinical databases based on rough set thoery, Information sciences, 112, 67-84, (1998)
[24] Wasilewska, A., Conditional knowledge representation systems–model for an implementation, Bulletin of the Polish Academy of sciences: mathematics, 37, 63-69, (1989) · Zbl 0753.68088
[25] Wybraniec-Skardowska, U., On a generalization of approximation space, Bulletin of the Polish Academy of sciences: mathematics, 37, 51-61, (1989) · Zbl 0755.04011
[26] Yao, Y.Y.; Lin, T.Y., Generalization of rough sets using modal logic, Intelligent automation and soft computing, an international journal, 2, 103-120, (1996)
[27] Yao, Y.Y., Constructive and algebraic methods of the theory of rough sets, Journal of information sciences, 109, 21-47, (1998) · Zbl 0934.03071
[28] Yao, Y.Y., Generalized rough set model, (), 286-318 · Zbl 0946.68137
[29] Yao, Y.Y., Relational interpretations of neighborhood operators and rough set approximation operators, Information sciences, 111, 239-259, (1998) · Zbl 0949.68144
[30] Yao, Y.Y., Combination of rough and fuzzy sets based on α-level sets, (), 301-321 · Zbl 0859.04005
[31] Ziarko, W., Variable precision rough set model, Journal of computer and system sciences, 46, 39-59, (1993) · Zbl 0764.68162
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