Fuzzy rough set theory for the interval-valued fuzzy information systems. (English) Zbl 1149.68434

Summary: The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory, i.e., the interval-valued fuzzy rough set model is presented based on the interval-valued fuzzy information systems which is defined in this paper by a binary interval-valued fuzzy relations \(R\in F^{(i)}(U\times U)\) on the universe \(U\). Several properties of the rough set model are given, and the relationships of this model and the others rough set models are also examined. Furthermore, we also discuss the knowledge reduction of the classical Pawlak information systems and the interval-valued fuzzy information systems respectively. Finally, the knowledge reduction theorems of the interval-valued fuzzy information systems are built.


68T37 Reasoning under uncertainty in the context of artificial intelligence
68T30 Knowledge representation
68U35 Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)
Full Text: DOI


[1] Banerjee, M.; Pal, S. K., Roughness of a fuzzy set, Information Sciences, 93, 235-246 (1996) · Zbl 0879.04004
[2] Beynon, M., Reducts with the variable precision rough sets model: a further investigation, European Journal of Operational Research, 134, 592-605 (2001) · Zbl 0984.90018
[3] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, International Journal of General System, 17, 2-3, 191-209 (1990) · Zbl 0715.04006
[4] Dubois, D.; Prade, H., Putting fuzzy sets and rough sets together, (Slowinski, R., Intelligent Decision Support (1992), Kluwer Academic: Kluwer Academic Dordrecht), 203-232
[5] Gorzalczany, B., Interval-valued fuzzy controller based on verbal modal of object, Fuzzy Sets and Systems, 28, 45-53 (1988) · Zbl 0662.93003
[7] Kondo, M., On the structure of generalized rough set, Information Sciences, 176, 589-600 (2006) · Zbl 1096.03065
[8] Kryszkiewicz, M., Rough set approach to incomplete information systems, Information Science, 112, 39-49 (1998) · Zbl 0951.68548
[9] Lin, T. Y., Granular computing on binary relation I: data mining and neighborhood systems, (Skowron, A.; Polkowski, L., Rough Sets in Knowledge Discovery (1998), Physica-Verlag), 107-121 · Zbl 0927.68089
[10] Marczewski, E., A general scheme of independence in mathematics, Bulletin de L Academie polonaise des Sciences Serie des Sciences Machematiques Astronomiques et physiques, 6, 731-736 (1958) · Zbl 0088.03001
[11] Morsi, N. N.; Yakout, M. M., Axiomatics for fuzzy rough sets, Fuzzy Sets and Systems, 100, 327-342 (1998) · Zbl 0938.03085
[12] Nanda, S.; Majumdar, S., Fuzzy rough sets, Fuzzy Sets and Systems, 45, 157-160 (1992) · Zbl 0749.04004
[13] Nakarnura, A., Fuzzy rough sets, Note on Multiple-valued Logic in Japan, 9, 8, 1-8 (1998)
[14] Orlowska, E., (Incomplete Information: Rough Set Analysis in Studies in Fuzziness and Soft Computing (1998), Springer)
[15] Pal, S. K.; Mitra, P., Case generation using rough sets with fuzzy representations, IEEE Transactions on Knowledge Data (2005)
[16] Pal, S. K., Soft data mining computational theory of perceptions and rough-fuzzy approach, Information Sciences, 163, 1-3, 5-12 (2004)
[17] Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11, 5, 341-356 (1982) · Zbl 0501.68053
[18] Pawlak, Z., Rough Set: Theoretical Aspects of Reasoning About Data (1991), Kluwer: Kluwer Norwell, MA · Zbl 0758.68054
[19] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Information Sciences, 177, 3-27 (2007) · Zbl 1142.68549
[20] Pawlak, Z.; Skowron, A., Rough sets: some extensions, Information Sciences, 177, 28-40 (2007) · Zbl 1142.68550
[21] Pawlak, Z.; Skowron, A., Rough sets and boolean reasoning, Information Sciences, 177, 41-73 (2007) · Zbl 1142.68551
[22] Quafafou, M., \(α\)-RST: a generalization of rough set theory, Information Sciences, 124, 301-316 (2000) · Zbl 0957.68114
[23] Skowron, A.; Polkowski, L., Rough Sets in Knowledge Discovery, vol. 12 (1998), Springer-Verlag · Zbl 0910.00028
[24] (Slowinski, R., Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Boston) · Zbl 0820.68001
[26] Turksen, B., Interval-valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, 20, 191-210 (1986) · Zbl 0618.94020
[27] Wang, Y. F., Mining stocking price using fuzzy rough set system, Expert System (2005)
[28] Wu, W. Z.; Mi, J. S.; Zhang, W. X., Generalized fuzzy rough sets, Information Science, 151, 263-282 (2003) · Zbl 1019.03037
[29] Yao, Y. Y., Constructive and algebraic methods of the theory of rough set, Information Sciences, 109, 21-47 (1998) · Zbl 0934.03071
[30] Yao, Y. Y., A comparative study of fuzzy sets and rough sets, Journal of Information Science, 109, 227-242 (1998) · Zbl 0932.03064
[32] Zhang, W. X.; Wu, W. Z.; Liang, J. Y.; Li, D. Y., Theory and Method of Rough Sets (2001), Science Press: Science Press Beijing
[33] Zhang, H. G.; Liang, H. L.; Liu, D. R., Two new operators in rough set theory with application to fuzzy sets, Information Sciences, 16, 147-165 (2004) · Zbl 1101.68871
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