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
Baczynski, M., Jayaram, B.: S- and R- implications: A state-of-the-art survey. Fuzzy Sets and Systems 159(14), 1836–1859 (2008)
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)
Bhatt, R.B., Gopal, M.: On the compact computational domain of fuzzy-rough sets. Pattern Recognition Letters 26, 1632–1640 (2005)
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)
Chouchoulas, A., Shen, Q.: Rough Set aided Keyword Reduction for Text categorization. Applied Artificial Intelligence 15, 843–873 (2001)
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)
Cornelis, C., Jensen, R., Hurtado, G., Slezak, D.: Attribute selection with fuzzy decision reducts. Information Sciences 180(2), 209–224 (2010)
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)
Dubois, D., Prade, H.: Rough fuzzy sets and Fuzzy Rough Sets. Int. J. General Systems 17(2-3), 191–209 (1990)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Jensen, R., Shen, Q.: Fuzzy Rough attribute reduction with application to web categorization. Fuzzy Sets and Systems 141(3), 469–485 (2004)
Jensen, R., Shen, Q.: Rough Sets, their Extensions and Applications. International Journal of Automation and Computing 4(3), 217–228 (2007)
Jensen, R., Shen, Q.: Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches. IEEE (2008)
Jensen, R., Shen, Q.: New approaches to fuzzy-rough feature selection. IEEE Transactions on Ruzzy Systems 17(4), 824–838 (2009)
Jensen’s repository of datasets, http://users.aber.ac.uk/rkj/datasets/index.php
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)
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)
Liu, Y., Xiong, R., Chu, J.: Quick Attribute Reduction Algorithm with Hash. Chinese Journal of Computers 32(8), 1493–1499 (2009)
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)
Marcus, S.: Tolerance Rough Sets, Cech topologies, learning processes. Bull. Polish Academy of Sciences, Technical Sciences 42(3), 471–487 (1994)
Matlab, http://www.mathworks.com
Nanda, S., Majumdar, S.: Fuzzy Rough Sets. Fuzzy Sets and Systems 45, 157–160 (1992)
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)
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)
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)
Nieminen, J.: Rough tolerance equality. Fundamenta Informaticae 11(3), 289–296 (1988)
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)
Olitos Dataset website at http://michem.disat.unimib.it/chm/download/datasets.htm#olit
Paul, S., Maji, P.: Fuzzy Discretization for Rough Set Based Gene Selection Algorithm. In: Proceedings of EAIT, pp. 317–320. IEEE (2011)
Pawlak, Z.: Rough Sets. International Journal of Computer and Information Science 11, 341–356 (1982)
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)
Pawlak, Z., Grzymala-Busse, J., Slowinski, R., Ziarko, W.: Rough Sets. Communications of ACM 38(11), 89–95 (1995)
Peters, J.F., Wasilewski, P.: Tolerance spaces: Origins, theoretical aspects and applications. Information Sciences 195, 211–225 (2012)
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)
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)
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)
Radzikowka, A.M., Kerre, E.E.: A comparative study of Fuzzy Rough Sets. Fuzzy Sets and Systems 126, 137–155 (2002)
Roy, A., Pal, S.K.: Fuzzy discretization of feature space for a rough set classifier. Pattern Recognition Letters 24(6), 895–902 (2003)
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)
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)
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
Skowron, A.: Rough Sets in KDD. In: Proceedings of the 16th World Computer Congress, Beijing, China, pp. 1–14 (2000)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)
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)
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)
Slowinski, R., Stefanowski, J.: Handling various types of Uncertainty in the Rough Set Approach. In: Proceedings of RSKD, pp. 366–376. Springer, Heidelberg (1993)
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)
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)
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)
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)
Tick, J., Fodor, J.: Fuzzy implications and inference processes. In: Proceedings of International Conference on Computational Cybernetics, pp. 105–109. IEEE (2005)
UCI Machine Learning Repository, http://archive.ics.uci.edu/ml/datasets.html
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)
Wei, W., Liang, J., Qian, Y.: A comparative study of rough sets for hybrid data. Information Sciences 190, 1–16 (2012)
Wikipedia on t-norm, http://en.wikipedia.org/wiki/T-norm
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)
Yao, Y.Y.: Relational interpretation of neighborhood operators and rough set approximation operators. Information Sciences 111(1-4), 239–259 (1998)
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)
Zhao, Y., Yao, Y., Luo, F.: Data analysis based on discernibility and indiscernibility. Information Sciences 177(22), 4959–4976 (2007)
Zhong, N., Dong, J.: Using Rough Sets with Heuristics for Feature Selection. Journal of Intelligent Information Systems 16, 199–214 (2001)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)
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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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