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Case Generation Using Rough Sets with Fuzzy Representation
March 2004 (vol. 16 no. 3)
pp. 292-300

Abstract—In this article, we propose a rough-fuzzy hybridization scheme for case generation. Fuzzy set theory is used for linguistic representation of patterns, thereby producing a fuzzy granulation of the feature space. Rough set theory is used to obtain dependency rules which model informative regions in the granulated feature space. The fuzzy membership functions corresponding to the informative regions are stored as cases along with the strength values. Case retrieval is made using a similarity measure based on these membership functions. Unlike the existing case selection methods, the cases here are cluster granules and not sample points. Also, each case involves a reduced number of relevant features. These makes the algorithm suitable for mining data sets, large both in dimension and size, due to its low-time requirement in case generation as well as retrieval. Superiority of the algorithm in terms of classification accuracy and case generation and retrieval times is demonstrated on some real-life data sets.

[1] J.L. Kolodner, Case-Based Reasoning. San Mateo, Calif.: Morgan Kaufmann, 1993.
[2] D.W. Aha, D. Kibler, and M.K. Albert, Instance-Based Learning Algorithms Machine Learning, vol. 6, pp. 37-66, 1991.
[3] D.R. Wilson and T.R. Martinez, Reduction Techniques for Instance-Based Learning Algorithms Machine Learning, vol. 38, no. 3, pp. 257-286, 2000.
[4] S.K. Pal, T.S. Dillon, and D.S. Yeung, Soft Computing in Case-Based Reasoning. London: Springer Verlag, 2000.
[5] H.-D. Burkhard and M.M. Richter, On the Notion of Similarity in Case Based Reasoning and Fuzzy Theory Soft Computing in Case-Based Reasoning, S.K. Pal, T.S. Dillon, and D.S. Yeung, eds., pp. 29-45, London: Springer Verlag, 2000.
[6] D. Dubois and H. Prade, Fuzzy Set Modeling in Case Based Reasoning Int'l J. Intelligent Systems, vol. 13, pp. 345-373, 1998.
[7] W. Dubitzky, A. Schuster, J. Hughes, and D. Bell, An Advanced Case Knowledge Architecture Based on Fuzzy Objects Applied Intelligence, vol. 7, pp. 187-204, 1997.
[8] R.K. De and S.K. Pal, A Connectionist Model for Selection of Cases Information Sciences, vol. 132, pp. 179-194, 2001.
[9] Z. Pawlak, Rough Sets Int'l J. Computer and Information Sciences, vol. 11, pp. 341-356, 1982.
[10] Z. Pawlak, Rough Sets, Theoretical Aspects of Reasoning about Data. Dordrecht: Kluwer Academic, 1991.
[11] L. Polkowski, A. Skowron, and J. Komorowski, Approximate Case-Based Reasoning: A Rough Mereological Approach Proc. Fourth German Workshop Case-Based Reasoning, System Deveolpment, and Evaluation, pp. 144-151, 1996.
[12] Proc. Int'l Workshop Rough Set Theory and Granular Computing. May 2001.
[13] Rough Fuzzy Hybridization: New Trends in Decision Making, S.K. Pal and A. Skowron, eds. Singapore: Springer Verlag, 1999.
[14] A. Skowron and C. Rauszer, The Discernibility Matrices and Functions in Information Systems Intelligent Decision Support, Handbook of Applications and Advances of the Rough Sets Theory, R. Slowiński, ed. pp. 331-362, Dordrecht: Kluwer Academic, 1992.
[15] S.K. Pal and S. Mitra, Multi-Layer Perceptron, Fuzzy Sets and Classification IEEE Trans. Neural Networks, vol. 3, pp. 683-697, 1992.
[16] S.K. Pal and S. Mitra, Neuro-Fuzzy Pattern Recognition: Methods in Soft Computing. New York: John Wiley, 1999.
[17] L.A. Zadeh, Calculus of Fuzzy Restrictions Fuzzy Sets and Their Applications to Cognitive and Decision Processes, L.A. Zadeh, K.S. Fu, K. Tanaka, and M. Shimura, eds. London: Academic Press, 1975.
[18] L.A. Zadeh, Outline of a New Approach to the Analysis of Complex Systems and Decision Processes IEEE Trans. Systems, Man, and Cybernetics, vol. 3, pp. 28-44, 1973.
[19] W. Pedrycz and Z.A. Sosnowski, Designing Decision Trees with the Use of Fuzzy Granulation IEEE Trans. Systems, Man, and Cybernetics, Part A: Systems and Humans, vol. 30, no. 2, pp. 151-159, 2000.
[20] L.A. Zadeh, Toward a Theory of Fuzzy Information Granulation and Its Centrality in Human Reasoning and Fuzzy Logic Fuzzy Sets and Systems, vol. 90, pp. 111-127, 1997.
[21] T.Y. Lin, Granular Computing: Fuzzy Logic and Rough Sets Computing with Words in Information/ Intelligent Systems, L.A. Zadeh and J. Kacprzyk, eds. pp. 183-200, Physica-Verlag, Heidelberg 1999.
[22] L.A. Zadeh, Fuzzy-Algorithmic Approach to the Definition of Complex or Imprecise Concepts J. Man-Machine Studies, vol. 8, pp. 249-291, 1976.
[23] M. Banerjee, S. Mitra, and S.K. Pal, Rough Fuzzy MLP: Knowledge Encoding and Classification IEEE Trans. Neural Networks, vol. 9, no. 6, pp. 1203-1216, 1998.
[24] T.Y. Lin and R. Chen, Finding Reducts in Very Large Databases Proc. Joint Conf. Information Science Research, pp. 350-352, 1997.
[25] C.L. Blake and C.J. Merz, UCI Repository of Machine Learning Databases, Univ. of California, Irvine, Dept. of Information and Computer Sciences, , 1998.
[26] D.W. Aha, Tolerating Noisy, Irrelevant, and Novel Attributes in Instance-Based Learning Algorithms Int'l J. Man-Machine Studies, vol. 36, pp. 267-287, 1992.

Index Terms:
Case-based reasoning, linguistic representation, rough dependency rules, granular computing, rough-fuzzy hybridization, soft computing, pattern recognition, data mining.
Sankar K. Pal, Pabitra Mitra, "Case Generation Using Rough Sets with Fuzzy Representation," IEEE Transactions on Knowledge and Data Engineering, vol. 16, no. 3, pp. 292-300, March 2004, doi:10.1109/TKDE.2003.1262181
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