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Triple-I FMP algorithm for double hierarchical fuzzy system based on manifold learning

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Abstract

As is well known, Zadeh presented the compositional rule of inference to discuss complex inference modes. After that other researchers also investigated this problem. However, the classic fuzzy control systems in the application often encounter the curse of dimensionality. To overcome these difficulties in the classic fuzzy control systems with high-dimensional input variables, the entire triple-I algorithm for double fuzzy control systems and manifold learning of dimensionality reduction will be discussed in this paper. Specifically, triple-I FMP algorithm is presented for double hierarchical fuzzy control system based on Guojun Wang’s implication operator and its reversibility is proved. Using manifold learning, dimension reduction SNE algorithm is given for double-layer hierarchical fuzzy control systems to keep the distribution of peak possibly point, so as to minimize the control stability impact due to reducing dimension. Since any type of multi-layer fuzzy control system is regarded as multiple fusion of double-layer hierarchical fuzzy system, the proposed algorithms and their reversibility are universal.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (nos. 61573173 and 61562050).

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Authors and Affiliations

  1. Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, Yunnan, People’s Republic of China

    Meng Li & Wenqi Liu

  2. Data Science Research Center, Kunming University of Science and Technology, Kunming, 650500, Yunnan, People’s Republic of China

    Meng Li & Wenqi Liu

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  1. Meng Li
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  2. Wenqi Liu
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Correspondence to Wenqi Liu.

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Li, M., Liu, W. Triple-I FMP algorithm for double hierarchical fuzzy system based on manifold learning. Int. J. Mach. Learn. & Cyber. 10, 2459–2466 (2019). https://doi.org/10.1007/s13042-018-0882-x

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  • DOI: https://doi.org/10.1007/s13042-018-0882-x

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