Interpretability improvement of RBF-based neurofuzzy systems using regularized learning

Radial-basis-function (RBF) networks are mathematically equivalent to a class of fuzzy systems under mild conditions. Therefore, RBF networks have widely been used in learning of neurofuzzy systems to improve the performance. However, in most cases, the interpretability of fuzzy system will get lost after neu­ ral network learning. This chapter proposes a learning method using interpretabil­ ity based regularization for neurofuzzy systems. This method can either be used in extracting interpretable fuzzy rules from RBF networks or in improving the interpretability of RBF-based neurofuzzy systems. Two simulation examples are presented to show the effectiveness of the proposed method.

[1]  Chuen-Tsai Sun,et al.  Functional equivalence between radial basis function networks and fuzzy inference systems , 1993, IEEE Trans. Neural Networks.

[2]  Hisao Ishibuchi,et al.  Multiobjective Optimization in Linguistic Rule Extraction from Numerical Data , 2001, EMO.

[3]  M. J. D. Powell,et al.  Radial basis functions for multivariable interpolation: a review , 1987 .

[4]  John E. Moody,et al.  Fast Learning in Multi-Resolution Hierarchies , 1988, NIPS.

[5]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[6]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[8]  Bernhard Sendhoff,et al.  On generating FC3 fuzzy rule systems from data using evolution strategies , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[9]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[10]  Mo-Yuen Chow,et al.  Heuristic constraints enforcement for training of and knowledge extraction from a fuzzy/neural architecture. I. Foundation , 1999, IEEE Trans. Fuzzy Syst..

[11]  Ahmad Lotfi,et al.  Interpretation preservation of adaptive fuzzy inference systems , 1996, Int. J. Approx. Reason..

[12]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[13]  Yaochu Jin,et al.  An approach to rule-based knowledge extraction , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[14]  Joachim Diederich,et al.  The truth will come to light: directions and challenges in extracting the knowledge embedded within trained artificial neural networks , 1998, IEEE Trans. Neural Networks.

[15]  J. Valente de Oliveira.  On the optimization of fuzzy systems using bio-inspired strategies , 1998 .

[16]  Jude W. Shavlik,et al.  Extracting Refined Rules from Knowledge-Based Neural Networks , 1993, Machine Learning.

[17]  Edward N. Lorenz,et al.  Irregularity: a fundamental property of the atmosphere* , 1984 .

[18]  Yoichi Hayashi,et al.  A Neural Expert System with Automated Extraction of Fuzzy If-Then Rules , 1990, NIPS.

[19]  Magne Setnes,et al.  Rule-based modeling: precision and transparency , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[20]  Yaochu Jin,et al.  Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement , 2000, IEEE Trans. Fuzzy Syst..