Extracting Interpretable Fuzzy Rules From RBF Networks

Fuzzy Systems and RBF Network

Fuzzy systems and radial-basis-function networks (RBFN) are functionally equivalent [1]. However, they are different in physical meanings. Fuzzy systems should satisfy the interpretability conditions whereas RBFN not. By comparing an interpretable fuzzy system and an RBF network, it has been found in [2] that the main difference between fuzzy systems and RBFNs is that fuzzy systems should share a certain number of their membership functions to reduce the number of fuzzy subsets in a fuzzy partition and therefore to improve the distinguishability of the fuzzy partition. Based on this observation, a regularization method has been proposed to extract fuzzy rules from RBFN [2]. This method can also be used to improve the interpretability of fuzzy systems that are generated from data.


[1] J.-S. R. Jang and C.-T. Sun. Functional equivalence between RBFN and fuzzy inference systems. IEEE Transactions on Neural Networks, 4:156-158, 1993
[2] Y. Jin, W. von Seelen and B. Sendhoff. Extracting interpretable fuzzy rules from RBF Neural Networks. Internal Report, IR-INI 2000-02, ISSN 0943-2752, Institut fuer Neuroinformatik, Ruhr-Universitaet Bochum, Bochum, January 2000
[3] Y. Jin, Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement. IEEE Transactions on Fuzzy Systems, 8(2):212-221, 2000

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