Structure of Covering-based Rough Sets

Authors: Shiping Wang, Peiyong Zhu, William Zhu

Abstract:

Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.

Keywords: Covering, poset, down-set, lattice, topological space, topological base.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080608

References:

[1] Zadeh, L.A.: Fuzzy sets. Information and Control 8 (1965) 338-353
[2] Liu, G., Sai, Y.: Invertible approximation operators of generalized rough sets and fuzzy rough sets. Information Sciences 180 (2010) 2221C2229
[3] Wang, F.Y.: Outline of a computational theory for linguistic dynamic systems: Toward computing with words. International Journal of Intelligent Control and Systems 2 (1998) 211-224
[4] Zadeh, L.: Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems 4 (1996) 103-111
[5] Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston (1991)
[6] Yao, Y.: Three-way decisions with probabilistic rough sets. Information Sciences 180 (2010) 341C353
[7] Bargiela, A., Pedrycz, W.: Granular Computing: an Introduction. Kluwer Academic Publishers, Boston (2002)
[8] Lin, T.Y.: Granular computing - structures, representations, and applications. In: LNAI. Volume 2639. (2003) 16-24
[9] Yao, Y.: Granular computing: basic issues and possible solutions. In: Proceedings of the 5th Joint Conference on Information Sciences. Volume 1. (2000) 186-189
[10] Yao, Y.: A partition model of granular computing. LNCS 3100 (2004) 232-253
[11] Iwinski, T.: Algebraic approach to rough sets. Bull. Polish Acad. Sci. Math. 35 (1987) 673-683
[12] Comer, S.: An algebraic approach to the approximation of information. Fundamenta Informaticae 14 (1991) 492-502
[13] Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27 (1996) 245-253
[14] Yao, Y.: Constructive and algebraic methods of theory of rough sets. Information Sciences 109 (1998) 21-47
[15] Yao, Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111 (1998) 239-259
[16] Zhu, F., Wang, F.Y.: Some results on covering generalized rough sets. Pattern Recognition and Artificial Intelligence 15 (2002) 6-13
[17] Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Information Sciences 152 (2003) 217-230
[18] Zhu, W., Wang, F.Y.: Properties of the third type of covering-based rough sets. In: ICMLC-07, Hong Kong, China, 19-22 August, 2007. (2007) 3746-3751
[19] Zhu, W.: Generalized rough sets based on relations. Information Sciences 177 (2007) 4997-5011
[20] Zhu, W., Wang, F.Y.: On three types of covering rough sets. IEEE Transactions on Knowledge and Data Engineering 19 (2007) 1131-1144
[21] Zhu, W.: Relationship among basic concepts in covering-based rough sets. Information Sciences 17 (2009) 2478-2486
[22] Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Information Sciences 179 (2009) 210-225
[23] Min, F., Liu, Q.: A hierarchical model for test-cost-sensitive decision systems. Information Sciences 179 (2009) 2442-2452
[24] Min, F., Liu, Q., , Fang, C.: Rough sets approach to symbolic value partition. International Jounal on Approximate Reasoning 49 (2008) 689-700
[25] Wang, S., Zhu, W., Zhu, P.: Poset approaches to covering-based rough sets. In: The fifth international conference on rough set and knowledge technology. (2010)
[26] Wang, S., Zhu, W., Zhu, P.: The covering upper approximation by subcovering. In: 2010 IEEE internation conference on granular and computing. (2010)
[27] Zhu, W.: Topological approaches to covering rough sets. Information Sciences 177 (2007) 1499-1508
[28] Liu, W.J., Bai, L., Jing, Q.: Some topological properties of rough approximation spaces. In: ICMLC 2006. (2006)
[29] Skowron, A.: On topology in information system. Bull. Polish Acad. Sci. Math. 36 (1988) 477-480
[30] Ge, X., Li, Z.: Definable subsets in covering approxiamtion spaces. International Journal of Computational and Mathematical Sciences 5 (2011) 31-34
[31] Rajagopal, P., Masone, J.: Discrete Mathematics for Computer Science. Saunders College, Canada (1992)