A Matrix Method for Calculation of the Approximations under the Asymmetric Similarity Relation Based Rough Sets

Abstract:

The essence of the rough set theory (RST) is to deal with the inconsistent problems by two definable subsets which are called the lower and upper approximations respectively. Asymmetric Similarity relation based Rough Sets (ASRS) model is one kind of extensions of the classical rough set model in incomplete information systems. In this paper, we propose a new matrix view of ASRS model and give the matrix representation of the lower and upper approximations of a concept under ASRS model. According to this matrix view, a new method is obtained for calculation of the lower and upper approximations under ASRS model. An example is given to illustrate processes of calculating the approximations of a concept based on the matrix point of view.

• Periodical: Advanced Materials Research (Volume 187)
• Pages: 251-256
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.187.251
• Online since: February 2011
• Authors: Lei Wang, Tian Rui Li, Jun Ye
• Keywords: Approximation, Asymmetric Similarity Relation, Incomplete Information System, Matrix, Rough Set (RS)

References

[1] Pawlak Z: Rough sets, International Journal of Computer and Information Science, 1982, 11: 341-356.

[2] Skowron A., Swiniarski R., and Synak P. Approximation Spaces and Information Granulation, Transaction on Rough Sets III, J. F. Peters, A. Skowron, and A. D. Van, (eds) Heidelberg: Springer Berlin, 2005, 3400: 175-189.

DOI: 10.1007/11427834_8

[3] Yao Y. Y., Wong S. K. M. A decision theoretic framework for approximating concepts, International Journal of Man-Machine Studies, 1992, 37(6): 793-809.

DOI: 10.1016/0020-7373(92)90069-w

[4] Kryszkiewicz M. Rules in incomplete information system. Information Sciences, 1999, 113(3-4): 271-292.

DOI: 10.1016/s0020-0255(98)10065-8

[5] Stefanowski J., Tsoukias A. On the extension of rough sets under Incomplete Information. Zhong N., Skowron A., Ohsuga S. Proceedings of the 7th International Workshop on New Directions in Rough Sets, Data Mining and Granular-Soft Computation. Yamaguchi: Physica-Verlag, 1999, 73-81.

DOI: 10.1007/978-3-540-48061-7_11

[6] Liu G. -L. The Axiomatization of the Rough Set Upper Approximation Operations, Fundamenta Informaticae, 2006, 69: 331-342.

[7] Wang L., Li T. R. Research on the Method of Calculation of Upper and Lower Approximations Based on Matrix, In: Proceedings of CRSSC-CWI-CGrC2010 (in Chinese), (2010).

[8] Liu Q. Rough Set and Rough Reasoning, Beijing: Science Press (in Chinese), (2001).

[9] Kryszkiewicz M. Rough set approach to incomplete information system. Information Sciences, 1998, 112: 39-49.

DOI: 10.1016/s0020-0255(98)10019-1

[10] Applied Mathematics of Tongji University, Linear Algebra (The fourth edition), Beijing: Higher Education Press (in Chinese), 2003, 29-38.