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Stability of hierarchical fuzzy systems generated by Neuro-Fuzzy

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Abstract

Hierarchical implementation provides a way of retaining the interpretability of a fuzzy system when the number of inputs to the system is very high. Existing Neuro-Fuzzy systems capable of constructing fuzzy systems from training data do not address this issue and restrict to the generation of single layer fuzzy systems. This paper first defines a generic hierarchical fuzzy system that can be implemented exploiting the recursion supported by standard programming languages. Secondly it shows that hierarchical fuzzy systems can be generated from a specialised multi-layer perceptron neural network using a heuristic rule extraction algorithm. Finally, the paper provides a proof for the stability of hierarchical fuzzy systems and the verification using simulation examples.

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Correspondence to R. Saad.

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Authors are affiliated with the Mechatronics Research Group, Department of Mechanical and Manufacturing Engineering, The University of Melbourne, Vic 3010, Australia. The second author contributed to this manuscript during his stay at Nanyang Technological University, School of Mechanical and Production Engineering on sabbatical leave from The University of Melbourne.

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Saad, R., Halgamuge, S. Stability of hierarchical fuzzy systems generated by Neuro-Fuzzy. Soft Computing 8, 409–416 (2004). https://doi.org/10.1007/s00500-003-0296-9

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  • DOI: https://doi.org/10.1007/s00500-003-0296-9

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