Rough Computational Approach to UAR based on Dominance Matrix in IOIS

Xiaoyan Zhang, Weihua Xu
DOI: 10.4236/iim.2011.34016                

Abstract

Rough set theory is a new mathematical tool to deal with vagueness and uncertainty. The classical rough set theory based on equivalence relation has made a great progress, while the equivalence relation is too harsh to meet and is extended to dominance relation in real world. It is important to investigate rough computational methods for rough set theory, which is one of the bottleneck problems in the development of rough set theory. In this article, rough computational approach to upper ap-proximation reduction (UAR) is discussed based on dominance matrix in inconsistent ordered information systems (IOIS). The algorithm of upper approximation reduction is obtained, from which we can provide approach to upper approximation reduction operated simply in inconsistent systems based on dominance relations. Finally, an example illustrates the validity of this method, and shows the method is excellent to a complicated information system.

Keywords

Dominance Relation, Information System, Rough Set, Upper Approximation Reduction

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Z. Pawlak, “Rough Sets,” International Journal of Computer and Information Science, Vol. 11, No. 5, 1982, pp. 341-356. doi:10.1007/BF01001956
[2]	Y. Leuang, W. Z. Wu and W. X. Zhang, “Knowledge Acquisition in Incomplete Information Systems: A Rough Set Approach,” European Journal of Operational Research, Vol. 168, No. 1, 2006, pp. 164-180.doi:10.1016/j.ejor.2004.03.032
[3]	W. H. Xu and W. X. Zhang, “Measuring Roughness of Generalized Rough Sets Induced by a Covering,” Fuzzy Sets and Systems, Vol. 158, No. 22, 2007, pp. 2443-2455.doi:10.1016/j.fss.2007.03.018
[4]	W. X. Zhang, W. Z. Wu, J. Y. Liang and D. Y. Li, “Theory and Method of Rough Sets,” Science Press, Beijing, 2001.
[5]	W. H. Xu, X. Y. Zhang and W. X. Zhang, “Upper Approximation Reduction in Inconsistent Information Systems Based on Dominance Relations,” Com-puter Engineering, Vol. 35, No. 18, 2009, pp. 191-193.
[6]	W. H. Xu, X. Y. Zhang and W. X. Zhang, “Knowledge Granula-tion, Knowledge Entropy and Knowledge Uncertainty Measure in Information Systems,” Applied Soft Computing, Vol. 9, No. 4, 2009, pp. 1244-1251. doi:10.1016/j.asoc.2009.03.007
[7]	W. H. Xu, X. Y. Zhang, J. M. Zhong and W. X. Zhang, “Attribute Reduction in Ordered Information Systems Based on Evidence Theory,” Knowledge and Information Systems, Vol. 25, No. 1, 2010, pp. 169-184. doi:10.1007/s10115-009-0248-5
[8]	W. H. Xu and W. X. Zhang, “Knowledge Reduction and Matrix Computation in Inconsistent Ordered Information Systems,” International Journal Business Intelligence and Data Mining, Vol. 3, No. 4, 2008, pp. 409-425.doi:10.1504/IJBIDM.2008.022737
[9]	W. H. Xu, M. W. Shao and W. X. Zhang, “Knowledge Reduction Based on Evidence Reasoning Theory in Ordered Information Systems,” Lecture Notes in Artificial Intelligence, Vol. 4092, 2006, pp. 535-547.
[10]	W. H. Xu and W. X. Zhang, “Methods for Knowledge Reduction in Inconsistent Ordered Information Systems,” Journal of Applied Mathematics & Computing, Vol. 26, No. 1-2, 2008, pp. 313-323.
[11]	W. Z. Wu, M. Zhang, H. Z. Li and J. S. Mi, “Attribute Reduction in Random Information Systems Via Dempster-Shafer Theory of Evidence,” In-formation Sciences, Vol. 174, No. 3-4, 2005, pp. 143-164. doi:10.1016/j.ins.2004.09.002
[12]	M. Zhang, L. D. Xu, W. X Zhang and H. Z. Li, “A Rough Set Approach to Knowledge Reduction Based on Inclusion Degree and Evidence Reasoning Theory,” Expert Systems, Vol. 20, No. 5, 2003, pp. 298-304. doi:10.1111/1468-0394.00254
[13]	S. Greco, B. Matarazzo and R. Slowingski, “Rough Approximation of a Preference Relatioin by Bominance Relatioin,” European Journal of Op-erational Research, Vol. 117, No. 1, 1999, pp. 63-83.doi:10.1016/S0377-2217(98)00127-1
[14]	S. Greco, B. Mata-razzo and R. Slowingski, “A New Rough Set Approach to Mul-ticriteria and Multiattribute Classificatioin. In: Rough Sets and Current Trends in Computing (RSCTC'98),” Springer-Verlag, Berlin, 1998. pp. 60-67.
[15]	S. Greco, B. Matarazzo and R. Slowingski, “Rough Sets Theory for Multicriteria Decision Analysis,” European Journal of Operational Research, Vol. 129, No. 1, 2001, pp. 11-47. doi:10.1016/S0377-2217(00)00167-3
[16]	S. Greco, B. Mata-razzo, R. Slowingski, “Rough Sets Methodology for Sorting Problems in Presence of Multiple Attributes and Criteria,” European Journal of Operational Research, Vol. 138, No. 2, 2002, pp. 247-259.doi:10.1016/S0377-2217(01)00244-2
[17]	K. Dembczynski, R. Pindur and R. Susmaga, “Generation of Exhaustive Set of Rules within Dominance- Based Rough Set Approach,” Electronic Notes Theory Compute Sciences, Vol. 82, No. 4, 2003.
[18]	Y. Sai, Y. Y. Yao and N. Zhong, “Data Analysis and Mining in Ordered Information Tables,” IEEE Computer Society Press, San Jose, 2001, pp. 497-504.
[19]	M. W. Shao and W. X. Zhang, “Dominance Relation and Rules in an In-complete Ordered Information System,” International Journal of Intelligent Systems, Vol. 20, No. 2005, pp. 13-27.doi:10.1016/S0377-2217(01)00244-2UUU