A modified gradient-based neuro-fuzzy learning algorithm and its convergence

Authors:
Wei Wu;Long Li;Jie Yang;Yan Liu
Affiliations:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Department of Applied Mathematics, Dalian Polytechnic University, Dalian 116034, China
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

Neuro-fuzzy approach is known to provide an adaptive method to generate or tune fuzzy rules for fuzzy systems. In this paper, a modified gradient-based neuro-fuzzy learning algorithm is proposed for zero-order Takagi-Sugeno inference systems. This modified algorithm, compared with conventional gradient-based neuro-fuzzy learning algorithm, reduces the cost of calculating the gradient of the error function and improves the learning efficiency. Some weak and strong convergence results for this algorithm are proved, indicating that the gradient of the error function goes to zero and the fuzzy parameter sequence goes to a fixed value, respectively. A constant learning rate is used. Some conditions for the constant learning rate to guarantee the convergence are specified. Numerical examples are provided to support the theoretical findings.