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A fuzzy system with common linear-term consequents equivalent to FLNN and GMM

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Abstract

In this study, a novel Takagi–Sugeno–Kang (TSK) fuzzy system termed as CLT–TSK in which the consequent of each fuzzy rule owns a common linear term is exploited to demonstrate its four distinctive merits. They are: (1) since much less parameters are involved, CLT–TSK has enhanced interpretability. (2) As an extensively used computational intelligence tool, a slightly changed function-link neural network (FLNN) is provably equivalent to CLT–TSK. As a result, FLNN is actually revisited with the first attempt from the philosophy of fuzzy models. (3) With a mild assumption that each component in Gaussian mixture model (GMM) equally contributes to the formulation of GMM in the sense of the effect of the intrinsic structure of training samples in each component on the corresponding label structure, CLT–TSK is theoretically proved to be equivalent to GMM, which actually helps us understand both CLT–TSK and FLNN from a new statistical perspective. (4) The output expression of CLT–TSK is exactly in accordance with the recently-drawn observation that a simple regression should be a basic yet very important component of final prediction models for various data modeling tasks. Owing to the equivalence among CLT–TSK, FLNN and GMM, their respective effective learning methods can be mutually employed from now on, and any new effort in training one model will actually provide a potential new learning method for another among these three models. In particular, with the help of our previous work about the least learning machine, we develop a fast-learning method for CLT–TSK in this study. Experimental results on different kinds of datasets demonstrate the promising classification and runtime performance of CLT–TSK.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 82072019, 61772198, and 61972181, by the Natural Science Foundation of Jiangsu Province under Grant BK20201441 and BK20191331, by Jiangsu Post-doctoral Research Funding Program under Grants with No. 2020Z020, and the Key Projects of the National Natural Science Foundation of China under Grant U20A20228.

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Authors and Affiliations

  1. Department of Medical Informatics, Nantong University, Nantong, 224001, China

    Yuanpeng Zhang

  2. School of Artificial Intelligence and Computer, Jiangnan University, Wuxi, 214122, China

    Shitong Wang

  3. Discipline of Information Technologies, Mathematics and Statistics, Murdoch University, Perth, Australia

    Guanjin Wang

  4. Department of Computing, The Hong Kong Polytechnical University, Hong Kong, China

    Yuanpeng Zhang & Fu-lai Chung

  5. Jiangsu Key Construction Laboratory of IoT Application Technology, Wuxi, China

    Shitong Wang

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  1. Yuanpeng Zhang
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  3. Fu-lai Chung
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  4. Shitong Wang
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Correspondence to Shitong Wang.

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Zhang, Y., Wang, G., Chung, Fl. et al. A fuzzy system with common linear-term consequents equivalent to FLNN and GMM. Int. J. Mach. Learn. & Cyber. 13, 1475–1492 (2022). https://doi.org/10.1007/s13042-021-01460-z

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