On Combining Neuro-Fuzzy Architectures with the Rough Set Theory to Solve Classification Problems with Incomplete Data

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-neuro-fuzzy classifier is derived. The architecture of the classifier is determined by the modified indexed center of gravity (MICOG) 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 implications. A theorem, which allows the determination of the structures of rough-neuro-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.

[1]  J. Fodor.  On fuzzy implication operators , 1991 .

[2]  Andrzej Bargiela,et al.  Granular clustering: a granular signature of data , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[3]  Robert Nowicki,et al.  Rough Sets in the Neuro-Fuzzy Architectures Based on Non-monotonic Fuzzy Implications , 2004, ICAISC.

[4]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[5]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning - II , 1975, Inf. Sci..

[6]  Chin-Teng Lin,et al.  Neural-Network-Based Fuzzy Logic Control and Decision System , 1991, IEEE Trans. Computers.

[7]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[8]  Nicole A. Lazar,et al.  Statistical Analysis With Missing Data , 2003, Technometrics.

[9]  Jerzy W. Grzymala-Busse,et al.  An overview of the LERS1 learning system , 1989, IEA/AIE '89.

[10]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[11]  Robert Nowicki.  Rough Sets in the Neuro-Fuzzy Architectures Based on Monotonic Fuzzy Implications , 2004, ICAISC.

[12]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[13]  Yiyu Yao,et al.  Induction of Classification Rules by Granular Computing , 2002, Rough Sets and Current Trends in Computing.

[14]  Masahiro Inuiguchi,et al.  Fuzzy rough sets and multiple-premise gradual decision rules , 2006, Int. J. Approx. Reason..

[15]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[16]  Masahiro Tanaka,et al.  Pattern classification by stochastic neural network with missing data , 1996, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929).

[17]  Detlef Nauck,et al.  Foundations Of Neuro-Fuzzy Systems , 1997 .

[18]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[19]  Jacek M. Zurada,et al.  Introduction to artificial neural systems , 1992 .

[20]  Phil D. Green,et al.  Robust automatic speech recognition with missing and unreliable acoustic data , 2001, Speech Commun..

[21]  Jacek M. Leski,et al.  Fuzzy and Neuro-Fuzzy Intelligent Systems , 2000, Studies in Fuzziness and Soft Computing.

[22]  A Reappraisal of Distance-Weighted K-Nearest Neighbor Classification for Pattern Recognition with Missing Data , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[23]  Christopher J. Merz,et al.  UCI Repository of Machine Learning Databases , 1996 .

[24]  D. Rutkowska,et al.  Implication-Based Neuro-Fuzzy Architectures , 2000 .

[25]  J. Recasens,et al.  UPPER AND LOWER APPROXIMATIONS OF FUZZY SETS , 2000 .

[26]  Jordi Recasens,et al.  Fuzzy groups, fuzzy functions and fuzzy equivalence relations , 2004, Fuzzy Sets Syst..

[27]  Jerzy W. Grzymala-Busse,et al.  LERS-A System for Learning from Examples Based on Rough Sets , 1992, Intelligent Decision Support.

[28]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[29]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[30]  Leszek Rutkowski,et al.  Flexible neuro-fuzzy systems , 2003, IEEE Trans. Neural Networks.

[31]  Pawan Lingras,et al.  Comparison of Neofuzzy and Rough Neural Networks , 1998, Inf. Sci..

[32]  Leszek Rutkowski,et al.  Neuro-Fuzzy Architectures with Various Implication Operators , 2000 .

[33]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control , 1994 .

[34]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[35]  Christopher J. C. Burges,et al.  A Tutorial on Support Vector Machines for Pattern Recognition , 1998, Data Mining and Knowledge Discovery.

[36]  Leszek Rutkowski,et al.  New Soft Computing Techniques for System Modeling, Pattern Classification and Image Processing , 2004 .

[37]  Olive Jean Dunn,et al.  Alternative Approaches to Missing Values in Discriminant Analysis , 1976 .

[38]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[39]  John K. Dixon,et al.  Pattern Recognition with Partly Missing Data , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[40]  Lawrence Carin,et al.  On Classification with Incomplete Data , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[41]  Zdzislaw Pawlak,et al.  Rough sets, decision algorithms and Bayes' theorem , 2002, Eur. J. Oper. Res..

[42]  Leszek Rutkowski,et al.  Designing and learning of adjustable quasi-triangular norms with applications to neuro-fuzzy systems , 2005, IEEE Transactions on Fuzzy Systems.

[43]  Pawan Lingras,et al.  Fuzzy-rough and rough-fuzzy serial combinations in neurocomputing , 2001, Neurocomputing.

[44]  Keon-Myung Lee,et al.  A fuzzy Neural Network Model for fuzzy Inference and Rule Tuning , 1994, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[45]  Hao Ying,et al.  Essentials of fuzzy modeling and control , 1995 .

[46]  Robert G. Reynolds,et al.  Evolutionary computation: Towards a new philosophy of machine intelligence , 1997 .

[47]  Didier Dubois,et al.  Putting Rough Sets and Fuzzy Sets Together , 1992, Intelligent Decision Support.

[48]  Jagath C. Rajapakse,et al.  Ovarian cancer classification with missing data , 2002, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02..

[49]  Marcelo Simoes.  Introduction to Fuzzy Control , 2003 .

[50]  J. Recasens,et al.  Fuzzy Equivalence Relations: Advanced Material , 2000 .