Properties and Approximation Distribution Reductions in Multigranulation Rough Set Model
Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1132058Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 405
 Z. Pawlak, “Rough sets and intelligent data analysis”, Information Sciences. Vol.147, no.1-4, pp.1-12, 2002.
 W. Roman, Q. Swiniarski and A. Skowron, “Rough Set Method in Feature Selection and Recognition”, Pattern Recognition Letters, vol.24 no.6 pp. 833-849, 2003.
 J.S. Mi, W.Z. Wu, W.X. Zhang, “Approaches to Approximation Reducts in Inconsistent Decision Tables”, G. Wang et al. (Eds.): RSFDGrC 2003, LNAI 2639, Springer-Verlag Berlin Heidelberg, pp. 283–286, 2003.
 M. Kryszkiewicz, “Rough Set Approach to Incomplete Information Systems”, Information Sciences, vol.112, no.1-4, pp.39-49, 1998.
 J. Stefanowski, “Incomplete Information Tables and Rough Classification”, Journal of Computational Intelligence, Vol.17, no.3, pp.545-566, 2001.
 G.Y. Wang, M.Y. Lu, “Variable precision rough set based decision tree classifier”, Journal of Intelligent and Fuzzy Systems, vol.23, no. 2-3, pp.61-70, 2012.
 J.Y. Leung, D. Y. Li, “Maximal consistent block technique for rule acquisition in incomplete information systems”, Information Sciences, vol.153, pp.86-106, 2003.
 C. Wu, X.B. Yang, “Information Granules in General and Complete Covering”, Proceedings of the 2005 IEEE International Conference on Granular Computing, pp. 675-678, 2005.
 W.L. Chen, J.X. Cheng, C.J. Zhang, “A Generalized Model of Rough Set Theory Based on Compatibility Relation”, Journal of computer engineering and applications, vol.16, no.4, pp.26-28, 2004.
 J.S. Mi, W.Z. Wu and W.X. Zhang, “Approaches to Knowledge Reduction Based on Variable Precision Rough Set Model”, Information Sciences, vol.159, no. 3-4, pp.255-272, 2004.
 C.W, X.Hu, Z. Li, X. Zhou, P. Achananuparp, “Algorithms for Different Approximations in Incomplete Information Systems with Maximal Compatible Classes as Primitive Granules”. Proc. of IEEE International Conference on Granular Computing, GrC 2007, San Jose, California, USA, pp.169-174, 2007.
 W. Xu, G.H. Zhang, W.X. Zhang, “Lower-approximation Distribution Reduct and Rules in Incomplete Information System”, Journal of Xi’an Institute of Technology (in Chinese), vol.24, No.4, pp.386-390, 2004.
 Y.H. Qian, J.Y. Liang, Y.Y. Yao, “MGRS: A multigranulation rough set”, Information Sciences, vol.180, no.6, pp.949–970, 2010.
 Y.H. Qian, J.Y. Liang, C.Y. Dang, “Incomplete multigranulation rough set”, IEEE Transactions on Systems, Man and Cybernetics, Part A, vol.40, no.2, pp.420-431, 2010.
 Y.H. Qian, J.Y. Liang, W. Wei, “Pessimistic rough decision”, in: Second International Workshop on Rough Sets Theory, Zhoushan, China, pp. 440–449, 2010.
 W. X. Zhang, J. S. Mi, W. Z. Wu, “Knowledge Reductions in Inconsistent Information Systems”, Chinese Journal of Computers(in Chinese), Vol.1, No.1, pp.12-18, 2003.
 L.J. Wang, X.B. Yang, J.Y. Yang, C. Wu, “Incomplete Decision Rule Acquisition Based on Multigranulation Theory”, Journal of Nanjing University of Science and Technology, Vol.37, No.1, pp.12-18, 2013.