Abstract and Applied Analysis

Granular Space Reduction to a β Multigranulation Fuzzy Rough Set

Junyi Zhou, Shaohui Ma, and Jianzhen Li

Full-text: Open access

Abstract

Multigranulation rough set is an extension of classical rough set, and optimistic multigranulation and pessimistic multigranulation are two special cases of it. β multigranulation rough set is a more generalized multigranulation rough set. In this paper, we first introduce fuzzy rough theory into β multigranulation rough set to construct a β multigranulation fuzzy rough set, which can be used to deal with continuous data; then some properties are discussed. Reduction is an important issue of multigranulation rough set, and an algorithm of granular space reduction to β multigranulation fuzzy rough set for preserving positive region is proposed. To test the algorithm, experiments are taken on five UCI data sets with different values of β. The results show the effectiveness of the proposed algorithm.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 679037, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412605762

Digital Object Identifier
doi:10.1155/2014/679037

Mathematical Reviews number (MathSciNet)
MR3193535

Citation

Zhou, Junyi; Ma, Shaohui; Li, Jianzhen. Granular Space Reduction to a β Multigranulation Fuzzy Rough Set. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 679037, 7 pages. doi:10.1155/2014/679037. https://projecteuclid.org/euclid.aaa/1412605762


Export citation

References

  • Y. Qian, J. Liang, and C. Dang, “Incomplete multigranulation rough set,” IEEE Transactions on Systems, Man, and Cybernetics A: Systems and Humans, vol. 40, no. 2, pp. 420–431, 2010.
  • Y. Qian, J. Liang, Y. Yao, and C. Dang, “MGRS: a multi-granulation rough set,” Information Sciences, vol. 180, no. 6, pp. 949–970, 2010.
  • Y. H. Qian, J. Y. Liang, and W. Wei, “Pessimistic rough decision,” Journal of Zhejiang Ocean University: Natural Science, vol. 25, no. 5, pp. 440–449, 2011.
  • Z. Pawlak, Rough Sets-Theoretical Aspects of Reasoning about Data, Springer, 1991.
  • Z. Pawlak and A. Skowron, “Rudiments of rough sets,” Information Sciences, vol. 177, no. 1, pp. 3–27, 2007.
  • Z. Pawlak and A. Skowron, “Rough sets: some extensions,” Information Sciences, vol. 177, no. 1, pp. 28–40, 2007.
  • Z. Pawlak and A. Skowron, “Rough sets and Boolean reasoning,” Information Sciences, vol. 177, no. 1, pp. 41–73, 2007.
  • W. Zhu, “Relationship between generalized rough sets based on binary relation and covering,” Information Sciences, vol. 179, no. 3, pp. 210–225, 2009.
  • W. Zhu and F.-Y. Wang, “On three types of covering-based rough sets,” IEEE Transactions on Knowledge and Data Engineering A: Systems and Humans, vol. 19, no. 8, pp. 1131–1143, 2007.
  • T. Y. Lin, “Granular computing I: the concept of granulation and its formal model,” International Journal of Granular Computing, Rough Sets and Intelligent Systems, vol. 1, no. 1, pp. 21–42, 2009.
  • X. Yang and M. Zhang, “Dominance-based fuzzy rough approach to an interval-valued decision system,” Frontiers of Computer Science in China, vol. 5, no. 2, pp. 195–204, 2011.
  • X. Yang and T. Y. Lin, “Knowledge operations in neighborhood system,” in Proceedings of the IEEE International Conference on Granular Computing (GrC '10), pp. 822–825, August 2010.
  • W. H. Xu, X. T. Zhang, and Q. R. Wang, “A generalized multi-granulation rough set approach,” in Bio-Inspired Computing and Applications, D.-S. Huang, Y. Gan, P. Premaratne, and K. Han, Eds., vol. 6840 of Lecture Notes in Bioinformatics, pp. 681–689, 2012.
  • W. Xu, Q. Wang, and X. Zhang, “Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space,” International Journal of Fuzzy Systems, vol. 13, no. 4, pp. 246–259, 2011.
  • Y. Qian, J. Liang, and C. Dang, “Incomplete multigranulation rough set,” IEEE Transactions on Systems, Man, and Cybernetics A: Systems and Humans, vol. 40, no. 2, pp. 420–431, 2010.
  • X. Yang, X. Song, H. Dou, and J. Yang, “Multi-granulation rough set: from crisp to fuzzy case,” Annals of Fuzzy Mathematics and Informatics, vol. 1, no. 1, pp. 55–70, 2011.
  • W. H. Xu, Q. R. Wang, and S. Q. Luo, “Mult i-granulat ion fuzzy rough sets,” Journal of Intelligent and Fuzzy Systems, vol. 26, pp. 1323–1340, 2014.
  • W. H. Xu, Q. R. Wang, and X. T. Zhang, “Multi-granulation rough sets based on tolerance relations,” Soft Computing, vol. 17, no. 7, pp. 1241–1252, 2013.
  • D. Dubios and H. Pradesets, “Rough fuzzy sets and fuzzy rough,” International Journal of General Systems, vol. 17, no. 2-3, pp. 191–209, 1990.
  • W. Xu, Y. Li, and X. Liao, “Approaches to attribute reductions based on rough set and matrix computation in inconsistent ordered information systems,” Knowledge-Based Systems, vol. 27, pp. 78–91, 2012.
  • 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, pp. 169–184, 2010.
  • J. Liang, F. Wang, C. Dang, and Y. Qian, “An efficient rough feature selection algorithm with a multi-granulation view,” International Journal of Approximate Reasoning, vol. 53, no. 6, pp. 912–926, 2012.
  • G. Lin, Y. Qian, and J. Li, “NMGRS: neighborhood-based multigranulation rough sets,” International Journal of Approximate Reasoning, vol. 53, no. 7, pp. 1080–1093, 2012.
  • Y. L. Sang and Y. H. Qian, “A granular space reduction approach to pessimistic multi-granulation rough sets,” Pattern Recognition and Artificial Intelligence, vol. 25, no. 3, pp. 361–366, 2012.
  • Q. Hu, D. Yu, and Z. Xie, “Information-preserving hybrid data reduction based on fuzzy-rough techniques,” Pattern Recognition Letters, vol. 27, no. 5, pp. 414–423, 2006. \endinput