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Issue No.09 - September (2008 vol.20)
pp: 1239-1253
Robert Nowicki , Czestochowa University of Technology, Czestochowa
This paper presents a new approach to fuzzy classification in the case of missing features. The rough set theory is incorporated into neuro-fuzzy structures and the rough-neurofuzzy classifier is derived. The architecture of the classifier is determined by the MICOG (modified indexed center of gravity) defuzzification method. The structure of the classifier is presented in a general form which includes both the Mamdani approach and the logical approach - based on the genuine fuzzy aplications. A theorem, which allows to determine the structures of a roughneuro-fuzzy classifiers based on the MICOG defuzzification, is given and proven. Specific rough-neuro-fuzzy structures based on the Larsen rule, the Reichenbach and the Kleene-Dienes implications are given in details. In the experiments it is shown that the classifier with the Dubois-Prade fuzzy implication is characterized by the best performance in the case of missing features
Decision support, Rule-based processing, Uncertainty, "fuzzy", and probabilistic reasoning, Fuzzy set, Classifier design and evaluation
Robert Nowicki, "On Combining Neuro-Fuzzy Architectures with the Rough Set Theory to Solve Classification Problems with Incomplete Data", IEEE Transactions on Knowledge & Data Engineering, vol.20, no. 9, pp. 1239-1253, September 2008, doi:10.1109/TKDE.2008.64
[1] D.B. Fogel, Evolutionary Computation: Towards a New Philosophy of Machine Intelligence. IEEE Press, 1995.
[2] D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Publishing, 1989.
[3] C.T. Lin and G.C.S. Lee, “Neural-Network-Based Fuzzy Logic Control and Decision System,” IEEE Trans. Computers, vol. 40, no. 12, pp. 1320-1336, Dec. 1991.
[4] L.X. Wang, Adaptive Fuzzy Systems and Control. PTR Prentice Hall, 1994.
[5] L.A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, pp. 338-353, 1965.
[6] L.A. Zadeh, “The Concept of a Linguistic Variable and Its Application to Approximate Reasoning: Part 1,” Information Sciences, vol. 8, pp. 199-249, 1975.
[7] C.M. Bishop, Neural Networks for Pattern Recognition. Clarendon Press, 1995.
[8] R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification. A Wiley-Interscience Publication, John Wiley & Sons, 2001.
[9] J.M. Zurada, Introduction to Artificial Neural Systems. West Publishing, 1992.
[10] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, 1992.
[11] W. Pedrycz and A. Bargiela, “Granular Clustering: A Granular Signature of Data,” IEEE Trans. Systems, Man, and Cybernetics —Part B, vol. 32, no. 2, pp. 212-224, Apr. 2002.
[12] J.T. Yao and Y.Y. Yao, “Induction of Classification Rules by Granular Computing,” Lecture Notes in Artificial Intelligence, vol. 2475, pp. 331-338, 2002.
[13] V. Kecman, Learning and Soft Computing, Support Vector Machines, Neural Networks and Fuzzy Logic Models. The MIT Press, 2001.
[14] C.J.C. Surges, “A Tutorial on Support Vector Machines for Pattern Recognition,” Data Mining and Knowledge Discovery, vol. 2, pp. 1-47, 1998.
[15] L.S. Chan and O.J. Dun, “Alternative Approaches to Missing Values in Discriminant Analysis,” J. Am. Statistical Assoc., vol. 71, pp. 842-844, 1976.
[16] J.K. Dixon, “Pattern Recognition with Partly Missing Data,” IEEE Trans. Systems, Man, and Cybernetics, vol. 9, no. 10, pp. 617-621, 1979.
[17] C. Renz, J.C. Rajapakse, K. Razvi, and S.K.C. Liang, “Ovarian Cancer Classification with Missing Data,” Proc. Ninth Int'l Conf. Neural Information Processing, (ICONIP '02), vol. 2, pp. 809-813, 2002.
[18] M. Tanaka, Y. Kotokawa, and T. Tanino, “Pattern Classification by Stochastic Neural Network with Missing Data,” Proc. IEEE Int'l Conf. System, Man and Cybernetics (SMC '96), vol. 1, pp. 690-695, 1996.
[19] R.L. Morin and D.E. Raeside, “A Reappraisal of Distance-Weighted K-Nearest Neighbor Classification for Pattern Recognition with Missing Data,” IEEE Trans. Systems, Man, and Cybernetics, vol. 11, pp. 241-243, 1981.
[20] M. Cooke, P. Green, L. Josifovski, and A. Vizinho, “Robust Automatic Speech Recognition with Missing and Unreliable Acoustic Data,” Speech Comm., vol. 34, no. 3, pp. 267-285, June 2001.
[21] R.J.A. Little and D.B. Rubin, Statistical Analysis with Missing Data, second ed. Wiley-Interscience, 2002.
[22] Z. Pawlak, “Rough Sets,” Int'l J. Information and Computer Science, vol. 11, no. 341, pp. 341-356, 1982.
[23] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, 1991.
[24] Z. Pawlak, “Rough Sets, Decision Algorithms and Bayes' Theorem,” European J. Operational Research, vol. 136, pp. 181-189, 2002.
[25] D. Dubois and H. Prade, “Rough Fuzzy Sets and Fuzzy Rough Sets,” Int'l J. General Systems, vol. 17, nos. 2-3, pp. 191-209, 1990.
[26] D. Dubois and H. Prade, “Putting Rough Sets and Fuzzy Sets Together,” Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, R. Slowiński, ed., pp. 203-232, Kluwer Academic Publishers, 1992.
[27] D. Boixader, J. Jacas, and J. Recasens, “Upper and Lower Approximation of Fuzzy Sets,” Proc. Seventh Int'l Fuzzy Systems Assoc. World Congress (IFSA '97), pp. 111-116, 1997.
[28] D. Boixader, J. Jacas, and J. Recasens, “Fuzzy Equivalence Relations: Advanced Material,” Fundamentals of Fuzzy Sets, P.Dubois, ed., pp. 261-290, Kluwer Academic Publishers, 1999.
[29] D. Boixader, J. Jacas, and J. Recasens, “Upper and Lower Approximation of Fuzzy Sets,” Int'l J. General Systems, vol. 29, pp. 555-568, 2000.
[30] M. Demirci and J. Recasens, “Fuzzy Groups, Fuzzy Functions and Fuzzy Equivalence Relations,” Fuzzy Sets and Systems, vol. 144, no. 3, pp. 441-458, 2004.
[31] S. Greco, M. Inuiguchi, and R. Słowiński, “Fuzzy Rough Sets and Multiple-Premise Gradual Decision Rules,” Int'l J. Approximate Reasoning, vol. 41, no. 2, pp. 179-211, 2006.
[32] R. Nowicki, “Rough Sets in the Neuro-Fuzzy Architectures Based on Monotonic Fuzzy Implications,” Lecture Notes in Artificial Intelligence, vol. 3070, pp. 510-517, 2004.
[33] R. Nowicki, “Rough Sets in the Neuro-Fuzzy Architectures Based on Non-Monotonic Fuzzy Implications,” Lecture Notes in Artificial Intelligence, vol. 3070, pp. 518-525, 2004.
[34] D. Williams, X. Liao, Y. Xue, L. Carin, and B. Krishnapuram, “On Classification with Incomplete Data,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 3, pp. 427-436, Mar. 2007.
[35] P. Lingras, “Comparison of Neofuzzy and Rough Neural Networks,” Information Sciences, vol. 110, nos. 3-4, pp. 207-215, Oct. 1998.
[36] P. Lingras, “Fuzzy-Rough and Rough-Fuzzy Serial Combinations in Neurocomputing,” Neurocomputing, vol. 36, nos. 1-4, pp. 29-44, Feb. 2001.
[37] E. Czogala and J. Leski, Fuzzy and Neuro-Fuzzy Intelligent Systems. Physica-Verlag, A Springer-Verlag Co., 2000.
[38] D. Driankov, H. Hellendoorn, and M. Reinfrank, An Introduction to Fuzzy Control. Springer-Verlag, 1993.
[39] D. Rutkowska and R. Nowicki, “Implication-Based Neuro-Fuzzy Architectures,” Int'l J. Applied Math. and Computer Science, vol. 10, no. 4, pp. 675-701, 2000.
[40] D. Rutkowska, R. Nowicki, and L. Rutkowski, “Neuro-Fuzzy Architectures with Various Implication Operators,” The State of the Art in Computational Intelligence, Proc. Int'l Symp. Computational Intelligence (ISCI '00), pp. 214-219, 2000.
[41] R.R. Yager and D.P. Filev, Essentials of Fuzzy Modeling and Control. John Wiley & Sons, 1994.
[42] K.M. Lee and D.H. Kwang, “A Fuzzy Neural Network Model for Fuzzy Inference and Rule Tuning,” Int'l J. Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 2, no. 3, pp. 265-277, 1994.
[43] D. Nauck, F. Klawonn, and R. Kruse, Foundations of Neuro-Fuzzy Systems. Wiley, 1997.
[44] R. Nowicki and D. Rutkowska, “Fuzzy Inference Neural Networks Based on Destructive and Constructive Approaches and Their Application to Classification,” Proc. Fourth Conf. Neural Network and Their Application, pp. 294-301, 1999.
[45] R. Nowicki, “The Neuro-Fuzzy Systems which Realizes Various Methods of Fuzzy Reasoning,” PhD dissertation, AGH Univ. of Science and Tech nology, May 2000. (in Polish).
[46] D. Rutkowska and R. Nowicki, “New Neuro-Fuzzy Architectures,” Proc. Int'l Conf. Artificial and Computational Intelligence for Decision, Control and Automation in Eng. and Industrial Applications (AcIDcA '00), pp. 82-87, Mar. 2000.
[47] L. Rutkowski, New Soft Computing Techniques for System Modeling, Pattern Classification and Image Processing. Springer, 2004.
[48] L. Rutkowski and K. Cpałka, “Flexible Neuro-Fuzzy Systems,” IEEE Trans. Neural Networks, vol. 14, no. 3, pp. 554-574, May 2003.
[49] L. Rutkowski and K. Cpałka, “Designing and Learning of Adjustable Quasi-Triangular Norms with Applications to Neuro-Fuzzy Systems,” IEEE Trans. Fuzzy Systems, vol. 13, no. 1, pp. 140-151, Feb. 2005.
[50] E.P. Klement, R. Mesiar, and E. Pap, Triangular Norms. Kluwer Academic Publishers, 2000.
[51] B. Schweizer and A. Sklar, “Associative Functions and Statistical Triangle Inequalities,” Publicationes Math. Debrecen, vol. 8, pp. 169-186, 1961.
[52] J.M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice Hall PTR, 2001.
[53] D. Rutkowska and R. Nowicki, “Constructive and Destructive Approach to Neuro Fuzzy Systems,” Proc. Joint Eurofuse-Soft and Intelligent Computing Conf. (EUROFUSE-SIC '99), pp. 100-105, 1999.
[54] J.C. Fodor, “On Fuzzy Implication,” Fuzzy Sets and Systems, vol. 42, pp. 293-300, 1991.
[55] D. Rutkowska, R. Nowicki, and L. Rutkowski, “Neuro-Fuzzy System with Inference Process Based on Zadeh Implication,” Proc. Third Int'l Conf. Parallel Processing and Applied Math. (PPAM '99), pp. 597-602, 1999.
[56] L. Polkowski, Rough Sets Mathematical Foundation. Physica-Verlag, A Springer-Verlag Co., 2002.
[57] C.J. Mertz and P.M. Murphy, “UCI Repository of Machine Learning Databases,” , 2008.
[58] J.W. Grzymala-Busse, “An Overview of the Lers1 Learning Systems,” Proc. Second Int'l Conf. Industrial and Eng. Applications of Artificial Intelligence and Expert Systems (IEA/AIE '89), pp. 838-844, 1989.
[59] J.W. Grzymala-Busse, “LERS—A System for Learning from Examples Based on Rough Sets,” Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, R.Slowinski, ed., pp. 3-18, Kluwer Academic Publishers, 1992.
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