×
Zhu, William

Relationship between generalized rough sets based on binary relation and covering. (English) Zbl 1163.68339

Inf. Sci. 179, No. 3, 210-225 (2009).
Summary: Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper systematically studies a type of generalized rough sets based on covering and the relationship between this type of covering-based rough sets and the generalized rough sets based on binary relation. Firstly, we present basic concepts and properties of this kind of rough sets. Then we investigate the relationships between this type of generalized rough sets and other five types of covering-based rough sets. The major contribution in this paper is that we establish the equivalency between this type of covering-based rough sets and a type of binary relation based rough sets. Through existing results in binary relation based rough sets, we present axiomatic systems for this type of covering-based lower and upper approximation operations. In addition, we explore the relationships among several important concepts such as minimal description, reduction, representative covering, exact covering, and unary covering in covering-based rough sets. Investigation of this type of covering-based will benefit to our understanding of other types of rough sets based on covering and binary relation.

Cited in 124 Documents

MSC:

68T30 Knowledge representation
68T37 Reasoning under uncertainty in the context of artificial intelligence

Keywords:

rough set; fuzzy set; granular computing; data mining; reduction; covering; approximation
PDF BibTeX XML Cite
\textit{W. Zhu}, Inf. Sci. 179, No. 3, 210--225 (2009; Zbl 1163.68339)
Full Text: DOI

References:

[1] Bargiela, A.; Pedrycz, W., Granular Computing: an Introduction (2002), Kluwer Academic Publishers: Kluwer Academic Publishers Boston
[2] Bartol, W.; Miro, J.; Pioro, K.; Rossello, F., On the coverings by tolerance classes, Inform. Sci., 166, 1-4, 193-211 (2004) · Zbl 1101.68863
[3] Bonikowski, Z.; Bryniarski, E.; Wybraniec-Skardowska, U., Extensions and intentions in the rough set theory, Inform. Sci., 107, 149-167 (1998) · Zbl 0934.03069
[4] Bryniarski, E., A calculus of rough sets of the first order, Bull. Pol. Acad. Sci., 36, 16, 71-77 (1989) · Zbl 0756.04002
[6] Dai, J., Rough 3-valued algebras, Inform. Sci., 178, 8, 1986-1996 (2008) · Zbl 1134.06008
[8] Deng, T.; Chen, Y.; Xu, W.; Dai, Q., A novel approach to fuzzy rough sets based on a fuzzy covering, Inform. Sci., 177, 2308-2326 (2007) · Zbl 1119.03051
[10] Li, J., Topological methods on the theory of covering generalized rough sets, Pattern Recogn. Artif. Intell., 17, 1, 7-10 (2004), (in Chinese)
[12] Lin, T. Y.; Liu, Q., Rough approximate operators: axiomatic rough set theory, (Ziarko, W., Rough Sets. Rough Sets, Fuzzy Sets and Knowledge Discovery (1994), Springer: Springer Berlin), 256-260 · Zbl 0818.03028
[14] Liu, G. L., The axiomatization of the rough set upper approximation operations, Fundam. Inform., 69, 23, 331-342 (2006) · Zbl 1096.68150
[15] Liu, G. L., Generalized rough sets over fuzzy lattices, Inform. Sci., 178, 6, 1651-1662 (2008) · Zbl 1136.03328
[16] Liu, G. L.; Zhu, W., The algebraic structures of generalized rough set theory, Inform. Sci., 178, 21, 4105-4113 (2008) · Zbl 1162.68667
[17] Mordeson, J., Rough set theory applied to (fuzzy) ideal theory, Fuzzy Sets Syst., 121, 315-324 (2001) · Zbl 1030.68085
[18] Pal, S. K.; Shankar, B. U.; Mitra, P., Granular computing, rough entropy and object extraction, Pattern Recogn. Lett., 26, 2509-2517 (2005)
[19] Pawlak, Z., Rough sets, Int. J. Comput. Inform. Sci., 11, 341-356 (1982) · Zbl 0501.68053
[20] Pawlak, Z., Rough Sets: Theoretical Aspects of Reasoning About Data (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Boston · Zbl 0758.68054
[21] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Inform. Sci., 177, 1, 3-27 (2007) · Zbl 1142.68549
[22] Pawlak, Z.; Skowron, A., Rough sets and Boolean reasoning, Inform. Sci., 177, 1, 41-73 (2007) · Zbl 1142.68551
[23] Pawlak, Z.; Skowron, A., Rough sets: some extensions, Inform. Sci., 177, 1, 28-40 (2007) · Zbl 1142.68550
[24] (Polkowski, L.; Skowron, A., Rough sets and current trends in computing, vol. 1424 (1998), Springer: Springer Berlin) · Zbl 0891.00026
[25] Pomykala, J. A., Approximation operations in approximation space, Bull. Pol. Acad. Sci., 35, 9-10, 653-662 (1987) · Zbl 0642.54002
[26] Skowron, A.; Stepaniuk, J., Tolerance approximation spaces, Fundam. Inform., 27, 245-253 (1996) · Zbl 0868.68103
[28] Slowinski, R.; Vanderpooten, D., A generalized definition of rough approximations based on similarity, IEEE Trans. Knowledge Data Eng., 12, 2, 331-336 (2000)
[30] Wang, F. Y., On the abstraction of conventional dynamic systems: from numerical analysis to linguistic analysis, Inform. Sci., 171, 233-259 (2005) · Zbl 1068.93010
[31] Wang, J.; Dai, D.; Zhou, Z., Fuzzy covering generalized rough sets, J. Zhoukou Teachers College, 21, 2, 20-22 (2004)
[32] Xu, Z.; Wang, Q., On the properties of covering rough sets model, J. Henan Normal Univ. (Nat. Sci.), 33, 1, 130-132 (2005) · Zbl 1091.03509
[36] Yao, Y. Y., Relational interpretations of neighborhood operators and rough set approximation operators, Inform. Sci., 111, 1-4, 239-259 (1998) · Zbl 0949.68144
[37] Yao, Y. Y., Constructive and algebraic methods of theory of rough sets, Inform. Sci., 109, 21-47 (1998) · Zbl 0934.03071
[41] Yao, Y. Y., Neighborhood systems and approximate retrieval, Inform. Sci., 176, 3431-3452 (2007) · Zbl 1119.68074
[42] Yeung, D.; Chen, D.; Tsang, E.; Lee, J.; Xizhao, W., On the generalization of fuzzy rough sets, IEEE Trans. Fuzzy Syst., 13, 3, 343-361 (2005)
[43] Zadeh, L. A., Fuzzy sets, Inform. Control, 8, 338-353 (1965) · Zbl 0139.24606
[44] Zadeh, L., Toward a generalized theory of uncertainty (GTU): an outline, Inform. Sci., 172, 1-2, 1-40 (2005) · Zbl 1074.94021
[45] Zakowski, W., Approximations in the space \((u, \pi)\), Demonstratio Math., 16, 761-769 (1983) · Zbl 0553.04002
[46] Zhong, N.; Dong, J. Z.; Ohsuga, S., Using rough sets with heuristics to feature selection, J. Intell. Inform. Syst., 16, 3, 199-214 (2001) · Zbl 0994.68149
[47] Zhong, N.; Yao, Y.; Ohshima, M., Peculiarity oriented multidatabase mining, IEEE Trans. Knowledge Data Eng., 15, 4, 952-960 (2003)
[48] Zhong, N., Rough sets in knowledge discovery and data mining, J. Jpn. Soc. Fuzzy Theory Syst., 13, 6, 581-591 (2001)
[49] Zhu, F.; He, H.-C., The axiomization of the rough set, Chin. J. Comput., 23, 3, 330-333 (2000)
[50] Zhu, W.; Wang, F.-Y., Reduction and axiomization of covering generalized rough sets, Inform. Sci., 152, 1, 217-230 (2003) · Zbl 1069.68613
[58] Zhu, W., Topological approaches to covering rough sets, Inform. Sci., 177, 6, 1499-1508 (2007) · Zbl 1109.68121
[61] Zhu, W., Generalized rough sets based on relations, Inform. Sci., 177, 22, 4997-5011 (2007) · Zbl 1129.68088
[62] Zhu, W.; Wang, F.-Y., On three types of covering rough sets, IEEE Trans. Knowledge Data Eng., 19, 8, 1131-1144 (2007)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.