On the Equivalence between Generalized Ellipsoidal Basis Function Neural Networks and T-S Fuzzy Systems
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This paper deals with the functional equivalence between Generalized Ellipsoidal Basis Function based Neural Networks (GEBF-NN) and T-S fuzzy systems. Significant contributions are summarized as follows. 1) The GEBF-NN is equivalent to a T-S fuzzy system under the condition that the GEBF unit and the local model correspond to the premise and the consequence of the T-S fuzzy system. 2) The normalized (nonnormalized) GEBF-NN is equivalent to a normalized (nonnormalized) T-S fuzzy system using dissymmetrical Gaussian functions (DGF) as univariate membership functions and local models as consequent parts. 3) The equivalence between the normalized GEBF-NN and the nonnormalized T-S fuzzy system is established by employing GEBF units as multivariate membership functions of fuzzy rules. 4) These theoretical results would not only fertilize the learning schemes for fuzzy systems but also enhance the interpretability of neural networks, and thereby contributing to innovative neuro-fuzzy paradigms. Finally, numerical examples are conducted to illustrate the main results.
Keywordsgeneralized ellipsoidal basis function neural network T-S fuzzy system functional equivalence
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