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Hybrid fuzzy polynomial neural networks with the aid of weighted fuzzy clustering method and fuzzy polynomial neurons

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Abstract

It is well-known that any nonlinear complex system can be modeled by using a collection of “if …then” fuzzy rules. In spite of a number of successful models reported in the literature, there are still two open issues: (1) one is not able to reflect the heterogeneous partition of the input space; (2) it becomes very difficult to deal effectively with high dimensionality of the problem (data). In this study, we present a parallel fuzzy polynomial neural networks (PFPNNs) with the aid of heterogeneous partition of the input space. Like fuzzy rules encountered in fuzzy models, the PFPNNs comprises a collection of premise and consequent parts. In the design of the premise part of the rule a weighted fuzzy clustering method is used not only to realize a nonuniform partition of the input space but to overcome a possible curse dimensionality. While in the design of consequent part, fuzzy polynomial neural networks are exploited to construct optimal local models (high order polynomials) that describe the relationship between the input variables and output variable within some local region of the input space. Two types of information granulation-based fuzzy polynomial neurons are developed for FPNNs. Particle swarm optimization (PSO) is employed to adjust the design parameters of parallel fuzzy polynomial neural networks. To evaluate the performance of PFPNNs a series of experiments based on several benchmarks are included. A comparative analysis demonstrates that the proposed model comes with higher accuracy and generalization capabilities in comparison with some previous models reported in the literature.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61301140, 61562024, 61673295) supported by the Open Foundation of State Key Laboratory of Digital Manufacturing & Technology (Grant No. DMETKF2015012), supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning [grant number NRF-2015R1A2A1A15055365], and also supported by the GRRC program of Gyeonggi province [GRRC Suwon 2016-B2, Center for U-city Security & Surveillance Technology].

Author information

Authors and Affiliations

  1. School of Computer and Communication Engineering, Tianjin University of Technology, Tianjin, 300384, China

    Wei Huang

  2. Department of Electrical Engineering, San 2-2 Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, South Korea

    Sung-Kwun Oh

  3. Department of Electrical & Computer Engineering, University of Alberta, Edmonton, T6R 2V4, AB, Canada

    Witold Pedrycz

  4. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Witold Pedrycz

  5. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Witold Pedrycz

Authors
  1. Wei Huang
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  2. Sung-Kwun Oh
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  3. Witold Pedrycz
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Corresponding author

Correspondence to Sung-Kwun Oh.

Appendix:

Appendix:

Five data sets with different complexities shown in Table 12 are included to further evaluate the performance of the PFPNN models [34–36]. The comparison of the PFPNNs and some other models are summarized in Table 13. MSE is used as the performance index.

Table 12 Descriptions of four machine learning data sets
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Table 13 Comparison of performance obtained for selected models
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Huang, W., Oh, SK. & Pedrycz, W. Hybrid fuzzy polynomial neural networks with the aid of weighted fuzzy clustering method and fuzzy polynomial neurons. Appl Intell 46, 487–508 (2017). https://doi.org/10.1007/s10489-016-0844-5

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  • DOI: https://doi.org/10.1007/s10489-016-0844-5

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