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Transactions on Rough Sets XVII pp 82–108Cite as

An Efficient Approach for Fuzzy Decision Reduct Computation

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Part of the book series: Lecture Notes in Computer Science ((TRS,volume 8375))

Abstract

Fuzzy rough sets is an extension of classical rough sets for feature selection in hybrid decision systems. However, reduct computation using the fuzzy rough set model is computationally expensive. A modified quick reduct algorithm (MQRA) was proposed in literature for computing fuzzy decision reduct using Radzikowska-Kerry fuzzy rough set model. In this paper, we develop a simplified computational model for discovering positive region in Radzikowska-Kerry’s fuzzy rough set model. Theory is developed for validation of omission of absolute positive region objects without affecting the subsequent inferences. The developed theory is incorporated in MQRA resulting in algorithm Improved MQRA (IMQRA). The computations involved in IMQRA are modeled as vector operations for obtaining further optimizations at implementation level. The effectiveness of algorithm(s) is empirically demonstrated by comparative analysis with several existing reduct approaches for hybrid decision systems using fuzzy rough sets.

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References

  1. Baczynski, M., Jayaram, B.: S- and R- implications: A state-of-the-art survey. Fuzzy Sets and Systems 159(14), 1836–1859 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bazan, J.G., Nguyen, H.S., Nguyen, S.H., Synak, P., Wroblewski, J.: Rough Set Algorithms in Classification Problem. In: Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.) Rough Set Methods and Applications. STUDFUZZ, vol. 56, pp. 49–88. Physica-Verlab GmbH, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Bhatt, R.B., Gopal, M.: On the compact computational domain of fuzzy-rough sets. Pattern Recognition Letters 26, 1632–1640 (2005)

    Article  Google Scholar 

  4. Blajdo, P., Grzymala-Busse, J.W., Hippe, Z.S., Knap, M., Mroczek, T., Piatek, L.: A Comparison of Six Approaches to Discretization—A Rough Set Perspective. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 31–38. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Chouchoulas, A., Shen, Q.: Rough Set aided Keyword Reduction for Text categorization. Applied Artificial Intelligence 15, 843–873 (2001)

    Article  Google Scholar 

  6. Cornelis, C., Cock, M.D., Radzikowska, A.M.: Fuzzy Rough Sets: from theory into practice. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 533–552. John Wiley and Sons (2008)

    Google Scholar 

  7. Cornelis, C., Jensen, R., Hurtado, G., Slezak, D.: Attribute selection with fuzzy decision reducts. Information Sciences 180(2), 209–224 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dubois, D., Prade, H.: Similarity versus Preference in Fuzzy Set-Based Logics. In: Incomplete Information: Rough Set Analysis. STUDFUZZ, vol. 13, pp. 441–461. Physica-Verlag, HD (1998)

    Chapter  Google Scholar 

  9. Dubois, D., Prade, H.: Rough fuzzy sets and Fuzzy Rough Sets. Int. J. General Systems 17(2-3), 191–209 (1990)

    Article  MATH  Google Scholar 

  10. Dubois, D., Prade, H.: Putting fuzzy sets and rough sets together. In: Slowiniski, R. (ed.) Intelligent Decision Support, pp. 203–232. Kluwer Academic, Dordrecht (1992)

    Chapter  Google Scholar 

  11. Duntsch, I., Gediga, G., Nguyen, H.S.: Rough set data analysis in the KDD process. In: Proceedings of IPMU, Madrid, Spain, pp. 220–226 (2000)

    Google Scholar 

  12. Fazayeli, F., Wang, L., Mandziuk, J.: Feature Selection Based on the Rough Set Theory and Expectation-Maximization Clustering Algorithm. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 272–282. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Greco, S., Matarazzo, B., Słowiński, R.: Fuzzy Similarity Relation as a Basis for Rough Approximations. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 283–289. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Henry, C.J., Ramanna, S.: Parallel computation in finding near neighbourhoods. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 523–532. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  15. Hu, Q.H., Xie, Z.X., Yu, D.R.: Fuzzy probabilistic approximation spaces and their information measures. IEEE Transactions on Fuzzy systems 14, 191–201 (2006)

    Article  Google Scholar 

  16. Hu, Q.H., Yu, D.R., Xie, Z.X.: Information preserving hybrid data reduction based on fuzzy rough techniques. Pattern Recognition Letters 27(5), 414–423 (2006)

    Article  Google Scholar 

  17. Hu, Q.H., Yu, D.R., Xie, Z.X.: Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recognition 40, 3509–3521 (2007)

    Article  MATH  Google Scholar 

  18. Ismail, M.K., Ciesielski, V.: An Empirical Investigation of the Impact of Discretization on Common Data Distributions. In: Proc. of HIS-2003 on Design and Application of Hybrid Intelligent Systems, pp. 692–701. IOS Press (2003)

    Google Scholar 

  19. Jensen, R., Shen, Q.: Fuzzy Rough attribute reduction with application to web categorization. Fuzzy Sets and Systems 141(3), 469–485 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Jensen, R., Shen, Q.: Rough Sets, their Extensions and Applications. International Journal of Automation and Computing 4(3), 217–228 (2007)

    Article  Google Scholar 

  21. Jensen, R., Shen, Q.: Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches. IEEE (2008)

    Google Scholar 

  22. Jensen, R., Shen, Q.: New approaches to fuzzy-rough feature selection. IEEE Transactions on Ruzzy Systems 17(4), 824–838 (2009)

    Article  Google Scholar 

  23. Jensen’s repository of datasets, http://users.aber.ac.uk/rkj/datasets/index.php

  24. Kretowski, M., Stepaniuk, J.: Selection of objects and attributes, a tolerance rough set approach. In: Proceedings of the Poster Session of Ninth International Symposium on Methodologies for Intelligent Systems, Zakopane Poland, pp. 169–180 (1996)

    Google Scholar 

  25. Lin, T.: Neighborhood systems and approximation in database and knowledge base sys-tems. In: Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems (1989)

    Google Scholar 

  26. Liu, Y., Xiong, R., Chu, J.: Quick Attribute Reduction Algorithm with Hash. Chinese Journal of Computers 32(8), 1493–1499 (2009)

    Google Scholar 

  27. Liu, W.-N., Yao, J., Yao, Y.: Rough approximations under level fuzzy sets. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 78–83. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  28. Marcus, S.: Tolerance Rough Sets, Cech topologies, learning processes. Bull. Polish Academy of Sciences, Technical Sciences 42(3), 471–487 (1994)

    MATH  Google Scholar 

  29. Matlab, http://www.mathworks.com

  30. Nanda, S., Majumdar, S.: Fuzzy Rough Sets. Fuzzy Sets and Systems 45, 157–160 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  31. Nguyen, H.S.: Discretization Problem for Rough Sets Methods. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 545–552. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  32. Nguyen, H.S.: On Exploring Soft Discretization of Continuous Attributes. In: Rough Neural Computing: Techniques for Computing with Words, Cognitive Technologies, pp. 333–350. Springer (2003)

    Google Scholar 

  33. Nguyen, H.S., Skowron, A.: Quantization of Real Value Attributes, Rough Set and Boolean Reasoning Approach. In: Proceedings of the 2nd Annual Joint Conference on Information Sciences, pp. 34–37 (1995)

    Google Scholar 

  34. Nieminen, J.: Rough tolerance equality. Fundamenta Informaticae 11(3), 289–296 (1988)

    MATH  MathSciNet  Google Scholar 

  35. Ningler, M., Stockmanns, G., Schneider, G., Dressler, O., Kochs, E.F.: Rough Set-Based Classification of EEG-Signals to Detect Intraoperative Awareness: Comparison of Fuzzy and Crisp Discretization of Real Value Attributes. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 825–834. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  36. Olitos Dataset website at http://michem.disat.unimib.it/chm/download/datasets.htm#olit

  37. Paul, S., Maji, P.: Fuzzy Discretization for Rough Set Based Gene Selection Algorithm. In: Proceedings of EAIT, pp. 317–320. IEEE (2011)

    Google Scholar 

  38. Pawlak, Z.: Rough Sets. International Journal of Computer and Information Science 11, 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  39. Pawlak, Z.: A treatise on rough sets. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS, vol. 3700, pp. 1–17. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  40. Pawlak, Z., Grzymala-Busse, J., Slowinski, R., Ziarko, W.: Rough Sets. Communications of ACM 38(11), 89–95 (1995)

    Article  Google Scholar 

  41. Peters, J.F., Wasilewski, P.: Tolerance spaces: Origins, theoretical aspects and applications. Information Sciences 195, 211–225 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  42. Peters, J.F., Ramanna, S.: Feature Selection: Near Set Approach. In: Raś, Z.W., Tsumoto, S., Zighed, D.A. (eds.) MCD 2007. LNCS (LNAI), vol. 4944, pp. 57–71. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  43. Qian, Y., Liang, J., Pedrycz, W., Dang, C.: Positive approximation: An accelerator for attribute reduction in rough set theory. Artificial Intelligence 174(9-10), 597–618 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  44. Qian, Y., Li, C., Liang, J.: An Efficient Fuzzy-Rough Attribute Reduction Approach. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 63–70. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  45. Radzikowka, A.M., Kerre, E.E.: A comparative study of Fuzzy Rough Sets. Fuzzy Sets and Systems 126, 137–155 (2002)

    Article  MathSciNet  Google Scholar 

  46. Roy, A., Pal, S.K.: Fuzzy discretization of feature space for a rough set classifier. Pattern Recognition Letters 24(6), 895–902 (2003)

    Article  MATH  Google Scholar 

  47. Sai Prasad, P.S.V.S., Rao, C.R.: IQuickReduct: An Improvement to Quick Reduct Algorithm. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 152–159. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  48. Sai Prasad, P.S.V.S., Raghavendra Rao, C.: Extensions to iQuickReduct. In: Sombattheera, C., Agarwal, A., Udgata, S.K., Lavangnananda, K. (eds.) MIWAI 2011. LNCS, vol. 7080, pp. 351–362. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  49. Sai Prasad, P.S.V.S., Rao, C.R.: Seed based fuzzy decision reduct for hybrid decision systems. In: Proceedings of FUZZ-IEEE, pp. 1–8. IEEE (2013), doi:10.1109/FUZZ-IEEE.2013.6622535

    Google Scholar 

  50. Skowron, A.: Rough Sets in KDD. In: Proceedings of the 16th World Computer Congress, Beijing, China, pp. 1–14 (2000)

    Google Scholar 

  51. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)

    MATH  MathSciNet  Google Scholar 

  52. Ślęzak, D., Betliński, P.: A Role of (Not) Crisp Discernibility in Rough Set Approach to Numeric Feature Selection. In: Hassanien, A.E., Salem, A.-B.M., Ramadan, R., Kim, T.-h. (eds.) AMLTA 2012. CCIS, vol. 322, pp. 13–23. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  53. Ślęzak, D., Wasilewski, P.: Granular Sets – Foundations and Case Study of Tolerance Spaces. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 435–442. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  54. Slowinski, R., Stefanowski, J.: Handling various types of Uncertainty in the Rough Set Approach. In: Proceedings of RSKD, pp. 366–376. Springer, Heidelberg (1993)

    Google Scholar 

  55. Slowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. Advances in Machine Intelligence & Soft Computing, Dept. of Electrical Engineering, Duke University, Durham, North Carolina, USA, 17–33 (1997)

    Google Scholar 

  56. Slowinski, R., Vanderpooten, D.: A Generalized Definition of Rough Approximations Based on Similarity. IEEE Transactions on Knowledge and Data Engineering 12(2), 331–336 (2000)

    Article  Google Scholar 

  57. Su, C.-T., Hsu, J.-H.: An Extended Chi2 Algorithm for Discretization of Real Value Attributes. IEEE Trans. on Knowledge and Data Engineering 17(3), 437–441 (2005)

    Article  Google Scholar 

  58. Tian, D., Zeng, X., Keane, J.: Core-generating approximate minimum entropy discretization for rough set feature selection in pattern classification. International Journal of Approximate Reasoning 52, 863–880 (2011)

    Article  Google Scholar 

  59. Tick, J., Fodor, J.: Fuzzy implications and inference processes. In: Proceedings of International Conference on Computational Cybernetics, pp. 105–109. IEEE (2005)

    Google Scholar 

  60. UCI Machine Learning Repository, http://archive.ics.uci.edu/ml/datasets.html

  61. Wang, X.Z., Tsang, E.C.C., Zhao, S.Y., Chen, D.G., Yeung, D.S.: Learning fuzzy rules from fuzzy samples based on rough set technique. Information Science 177, 4493–4514 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  62. Wei, W., Liang, J., Qian, Y.: A comparative study of rough sets for hybrid data. Information Sciences 190, 1–16 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  63. Wikipedia on t-norm, http://en.wikipedia.org/wiki/T-norm

  64. Yao, Y.Y.: Combination of rough and fuzzy sets based on α-level sets. In: Lim, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 301–321. Kluwer Academic Publishers, Boston (1997)

    Chapter  Google Scholar 

  65. Yao, Y.Y.: Relational interpretation of neighborhood operators and rough set approximation operators. Information Sciences 111(1-4), 239–259 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  66. Zhao, Y., Luo, F., Wong, S.K.M., Yao, Y.: A general definition of an attribute reduct. In: Yao, J., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślęzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 101–108. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  67. Zhao, Y., Yao, Y., Luo, F.: Data analysis based on discernibility and indiscernibility. Information Sciences 177(22), 4959–4976 (2007)

    Article  MATH  Google Scholar 

  68. Zhong, N., Dong, J.: Using Rough Sets with Heuristics for Feature Selection. Journal of Intelligent Information Systems 16, 199–214 (2001)

    Article  MATH  Google Scholar 

  69. Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Computer and Information Sciences, University of Hyderabad, Hyderabad, Andhra Pradesh, India

    P. S. V. S. Sai Prasad & C. Raghavendra Rao

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  1. P. S. V. S. Sai Prasad
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  2. C. Raghavendra Rao
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  1. Computational Intelligence Laboratory, ECE Department, University of Manitoba, MB R3T 5V6, Winnipeg, Canada

    James F. Peters

  2. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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Sai Prasad, P.S.V.S., Raghavendra Rao, C. (2014). An Efficient Approach for Fuzzy Decision Reduct Computation. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets XVII. Lecture Notes in Computer Science, vol 8375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54756-0_5

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