Applied Intelligence

, Volume 46, Issue 2, pp 487–508 | Cite as

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

  • Wei Huang
  • Sung-Kwun OhEmail author
  • Witold Pedrycz


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.


Parallel fuzzy polynomial neural networks (PFPNNs) Fuzzy polynomial neural networks (FPNNs) Weighted fuzzy clustering method (WFCM) Particle swarm optimization (PSO) 



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].


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Computer and Communication EngineeringTianjin University of TechnologyTianjinChina
  2. 2.Department of Electrical EngineeringHwaseong-siSouth Korea
  3. 3.Department of Electrical & Computer EngineeringUniversity of AlbertaEdmontonCanada
  4. 4.Systems Research Institute, Polish Academy of SciencesWarsawPoland
  5. 5.Department of Electrical and Computer Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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