On the equivalence between generalized ellipsoidal basis function neural networks and t-s fuzzy systems

Authors:
Ning Wang;Min Han;Nuo Dong;Meng Joo Er;Gangjian Liu
Affiliations:
Marine Engineering College, Dalian Maritime University, Dalian, China;Faculty of EIEE, Dalian University of Technology, Dalian, China;Marine Engineering College, Dalian Maritime University, Dalian, China;Marine Engineering College, Dalian Maritime University, Dalian, China,School of EEE, Nanyang Technological University, Singapore;Marine Engineering College, Dalian Maritime University, Dalian, China
Venue:
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part II
Year:
2013

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Abstract

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.