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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 946070, 12 pages
http://dx.doi.org/10.1155/2013/946070
Research Article

Test-Cost-Sensitive Attribute Reduction of Data with Normal Distribution Measurement Errors

Laboratory of Granular Computing, Zhangzhou Normal University, Zhangzhou 363000, China

Received 31 December 2012; Accepted 1 March 2013

Academic Editor: Hung Nguyen-Xuan

Copyright © 2013 Hong Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Bell, A Beginner's Guide to Uncertainty of Measurement, National Physical Laboratory, 2001.
  2. C. C. Aggarwal, “On density based transforms for uncertain data mining,” in Proceedings of IEEE 23rd International Conference on Data Engineering (ICDE '07), pp. 866–875, April 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Chau, R. Cheng, B. Kao, and J. Ng, “Uncertain data mining: an example in clustering location data,” in Proceedings of the 10th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD '06), vol. 3918 of Lecture Notes in Computer Science, pp. 199–204, 2006.
  4. F. Min and W. Zhu, “Attribute reduction of data with error ranges and test costs,” Information Sciences, vol. 211, pp. 48–67, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. W. Fan, S. Stolfo, J. Zhang, and P. Chan, “Adacost: misclassification cost-sensitive boosting,” in Proceedings of the 16th International Conference on Machine Learning (ICML '99), 1999.
  6. F. Min, H. P. He, Y. H. Qian, and W. Zhu, “Test-cost-sensitive attribute reduction,” Information Sciences, vol. 181, pp. 4928–4942, 2011. View at Google Scholar
  7. F. Min and Q. Liu, “A hierarchical model for test-cost-sensitive decision systems,” Information Sciences, vol. 179, no. 14, pp. 2442–2452, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Pazzani, C. Merz, P. M. K. Ali, T. Hume, and C. Brunk, “Reducing misclassification costs,” in Proceedings of the 11th International Conference of Machine Learning (ICML' 94), Morgan Kaufmann, 1994.
  9. H. Zhao, F. Min, and W. Zhu, “Test-cost-sensitive attribute reduction based on neighborhood rough set,” in Proceedings of the IEEE International Conference on Granular Computing, 2011.
  10. Z. H. Zhou and X. Y. Liu, “Training cost-sensitive neural networks with methods addressing the class imbalance problem,” IEEE Transactions on Knowledge and Data Engineering, vol. 18, no. 1, pp. 63–77, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. Y. Yao and Y. Zhao, “Attribute reduction in decision-theoretic rough set models,” Information Sciences, vol. 178, no. 17, pp. 3356–3373, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Dash and H. Liu, “Consistency-based search in feature selection,” Artificial Intelligence, vol. 151, no. 1-2, pp. 155–176, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. Y. Jia, W. H. Liao, Z. M. Tang, and L. Shang, “Minimum cost attribute reduction in decision-theoretic rough set models,” Information Sciences, vol. 219, pp. 151–167, 2013. View at Google Scholar
  14. H. X. Li, X. Z. Zhou, J. B. Zhao, and D. Liu, “Attribute reduction in decision-theoretic rough set model: a further investigation,” in Proceedings of Rough Sets and Knowledge Technology, vol. 6954 of Lecture Notes in Computer Science, 2011.
  15. Y. Y. Yao, Y. Zhao, and J. Wang, “On reduct construction algorithms,” in Proceedings of the Rough Sets and Knowledge Technology (RSKT '06), vol. 4062, pp. 297–304, 2006.
  16. W. Zhu and F.-Y. Wang, “Reduction and axiomization of covering generalized rough sets,” Information Sciences, vol. 152, pp. 217–230, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. L. W. Ma, “On some types of neighborhood-related covering rough sets,” International Journal of Approximate Reasoning, vol. 53, no. 6, pp. 901–911, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. W. Zhu, “Generalized rough sets based on relations,” Information Sciences, vol. 177, no. 22, pp. 4997–5011, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. W. Zhu, “Topological approaches to covering rough sets,” Information Sciences, vol. 177, no. 6, pp. 1499–1508, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. W. Zhu, “Relationship among basic concepts in covering-based rough sets,” Information Sciences, vol. 179, no. 14, pp. 2478–2486, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. W. Zhu, “Relationship between generalized rough sets based on binary relation and covering,” Information Sciences, vol. 179, no. 3, pp. 210–225, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. W. Zhu and F. Wang, “Covering based granular computing for conflict analysis,” in Intelligence and Security Informatics, vol. 3975 of Lecture Notes in Computer Science, pp. 566–571, 2006.
  23. W. Zhu and F. Y. Wang, “On three types of covering-based rough sets,” IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 8, pp. 1131–1143, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. Q. Hu, W. Pedrycz, D. R. Yu, and J. Lang, “Selecting discrete and continuous features based on neighborhood decision error minimization,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 40, no. 1, pp. 137–150, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. Q. H. Hu, D. R. Yu, J. F. Liu, and C. Wu, “Neighborhood rough set based heterogeneous feature subset selection,” Information Sciences, vol. 178, no. 18, pp. 3577–3594, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. Q. H. Hu, D. R. Yu, and Z. X. Xie, “Numerical attribute reduction based on neighborhood granulation and rough approximation,” Journal of Software, vol. 19, no. 3, pp. 640–649, 2008 (Chinese). View at Publisher · View at Google Scholar · View at Scopus
  27. H. X. Li, M. H. Wang, X. Z. Zhou, and J. B. Zhao, “An interval set model for learning rules from incomplete information table,” International Journal of Approximate Reasoning, vol. 53, no. 1, pp. 24–37, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. W. Wei, J. Liang, and Y. Qian, “A comparative study of rough sets for hybrid data,” Information Sciences, vol. 190, pp. 1–16, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. F. Min, W. Zhu, H. Zhao, G. Y. Pan, J. B. Liu, and Z. L. Xu, “Coser: Cost-senstive rough sets,” 2012, http://grc.fjzs.edu.cn/~fmin/coser/.
  30. Wikipedia, http://www.wikipedia.org/.
  31. H. Zhao, F. Min, and W. Zhu, “Inducing covering rough sets from error distribution,” Journal of Information & Computational Science, vol. 10, no. 3, pp. 851–859, 2013. View at Google Scholar
  32. P. Zhu, “Covering rough sets based on neighborhoods: an approach without using neighborhoods,” International Journal of Approximate Reasoning, vol. 52, no. 3, pp. 461–472, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. Y. Chen, D. Miao, and R. Wang, “A rough set approach to feature selection based on ant colony optimization,” Pattern Recognition Letters, vol. 31, no. 3, pp. 226–233, 2010. View at Publisher · View at Google Scholar · View at Scopus
  34. Q. Hu, S. An, and D. Yu, “Soft fuzzy rough sets for robust feature evaluation and selection,” Information Sciences, vol. 180, no. 22, pp. 4384–4400, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. Y. Du, Q. Hu, P. F. Zhu, and P. J. Ma, “Rule learning for classification based on neighborhood covering reduction,” Information Sciences, vol. 181, no. 24, pp. 5457–5467, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  36. Y. H. Qian, J. Y. Liang, and C. Y. Dang, “Converse approximation and rule extraction from decision tables in rough set theory,” Computers & Mathematics with Applications, vol. 55, no. 8, pp. 1754–1765, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  37. X. B. Yang, D. J. Yu, J. Y. Yang, and X. N. Song, “Difference relation-based rough set and negative rules in incomplete information system,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 17, no. 5, pp. 649–665, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. Z. Pawalk, “Rough sets: theoretical aspects of reasoning about data,” 1991.
  39. Z. Pawlak and A. Skowron, “Rough sets: some extensions,” Information Sciences, vol. 177, no. 1, pp. 28–40, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  40. W. Z. Wu and Y. Leung, “Theory and applications of granular labelled partitions in multi-scale decision tables,” Information Sciences, vol. 181, no. 18, pp. 3878–3897, 2011. View at Google Scholar
  41. Y. Qian, J. Liang, D. Li, H. Zhang, and C. Dang, “Measures for evaluating the decision performance of a decision table in rough set theory,” Information Sciences, vol. 178, no. 1, pp. 181–202, 2008. View at Publisher · View at Google Scholar · View at Scopus
  42. R. B. Barot and T. Y. Lin, “Granular computing on covering from the aspects of knowledge theory,” in Proceedings of the IEEE Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS '08), May 2008. View at Publisher · View at Google Scholar · View at Scopus
  43. S. Calegari and D. Ciucci, “Granular computing applied to ontologies,” International Journal of Approximate Reasoning, vol. 51, no. 4, pp. 391–409, 2010. View at Publisher · View at Google Scholar · View at Scopus
  44. T. Y. Lin, “Granular computing: practices, theories, and future directions,” Encyclopedia of Complexity and Systems Science, vol. 2009, pp. 4339–4355, 2009. View at Google Scholar
  45. L. Zadeh, “Fuzzy sets and information granularity,” Advances in Fuzzy Set Theory and Applications, vol. 11, pp. 3–18, 1979. View at Google Scholar
  46. A. Bargiela and W. Pedrycz, Granular Computing: An Introduction, Kluwer Academic, Boston, Mass, USA, 2003. View at Zentralblatt MATH · View at MathSciNet
  47. T. Y. Lin, “Granular computing on binary relations-analysis of conflict and chinese wall security policy,” in Proceedings of the Rough Sets and Current Trends in Computing, vol. 2475 of Lecture Notes in Computer Science, 2002.
  48. T. Y. Lin, “Granular computing structures, representations, and applications,” in Proceedings of the 9th International Conference (RSFDGrC '03), vol. 2639 of Lecture Notes in Artificial Intelligence, pp. 16–24, May 2003. View at Scopus
  49. Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, no. 5, pp. 341–356, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  50. Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic, Boston, Mass, USA, 1991.
  51. J. G. Bazan and A. Skowron, “Dynamic reducts as a tool for extracting laws from decision tables,” in Proceedings of the 8th International Symposium on Methodologies for Intelligent Systems, 1994.
  52. Y. H. Qian, J. Y. Liang, W. Pedrycz, and C. Y. Dang, “Positive approximation: an accelerator for attribute reduction in rough set theory,” Artificial Intelligence, vol. 174, no. 9-10, pp. 597–618, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  53. C. L. Blake and C. J. Merz, “UCI repository of machine learning databases,” 1998, http://www.ics.uci.edu/~mlearn/mlrepository.html.