Advertisement

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
Article

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.

Keywords

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

Notes

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].

References

  1. 1.
    Srinivasan D, Chan CW, Balaji PG (2009) Computational Intelligence-based Congestion Prediction for a Dynamic Urban Street Network. Neurocomputing 72:2710–2716CrossRefGoogle Scholar
  2. 2.
    Roh SB, Oh SK (2014) Polynomial Fuzzy Radial Basis Function Neural Networks Classifier Realized with the aid of Boundary Area Decision. J Electr Eng Technol 9(6):2098–2106CrossRefGoogle Scholar
  3. 3.
    Guo Z, Wu Z, Dong X, Wang K, Zhang S, Li Y (2014) Component thermos dynamical selection based gene expression programming for function finding. Math Probl Eng 2014:1–16Google Scholar
  4. 4.
    Guo Z, Wang S, Yue X, Yang H (2015) Global harmony search with generalized opposition-based learning. Soft Comput 15:1–9Google Scholar
  5. 5.
    Wang D, Xiong C, Zhang X (2015) An opposition-based group search optimizer with diversity guidance. Math Probl Eng 2015 :1–12Google Scholar
  6. 6.
    Pawinski G, Sapiecha K (2016) Speeding up global optimization with the help of intelligence supervisors. Appl Intell 45:1–16CrossRefGoogle Scholar
  7. 7.
    Mollov S, Babuska R, Abonyi J, Verbruggen HB (2004) Effective Optimization for Fuzzy Model Predictive Control. IEEE Trans Fuzzy Syst 12:661–675CrossRefGoogle Scholar
  8. 8.
    Lam HK, Narimani M (2010) Quadratic-Stability Analysis of Fuzzy-model-based Control Systems using Staircase Membership Functions. IEEE Trans Fuzzy Syst 18:125–137CrossRefGoogle Scholar
  9. 9.
    Li C, Zhou J, Fu B, Kou P, Xiao J (2012) T-S fuzzy model identification with a gravitational search-based hyperplane clustering algorithm. IEEE Trans Fuzzy Syst 20:305–317CrossRefGoogle Scholar
  10. 10.
    Hathaway RJ, Bezdek JC (2000) Generalized fuzzy c-means clustering strategies using LP norm distances. IEEE Trans Fuzzy Syst 8:576–582CrossRefGoogle Scholar
  11. 11.
    Yu J, Cheng Q, Huang H (2004) Analysis of the weighting exponent in the FCM. IEEE Trans Syst Man Cybern Part B Cybern 34:634–639CrossRefGoogle Scholar
  12. 12.
    Huang W, Wang J, Liao J (2016) A granular classifier by means of context-based similarity clustering. J Electr Eng Technol 11:993–1004CrossRefGoogle Scholar
  13. 13.
    Tuan TM, Ngan TT, Son LH (2016) A novel semi-supervised fuzzy clustering method based on interactive fuzzy satisfying for dental x-ray image segmentation. Appl Intell 45:1–14CrossRefGoogle Scholar
  14. 14.
    Ivakhnenko AG, Ivakhnenko GA (1995) The Review of Problems Solvable by Algorithms of the Group Method of Data Handling (GMDH). Pattern Recogn Image Anal 5(3):527–535Google Scholar
  15. 15.
    Oh S-K, Pedrycz W (2003) Fuzzy Polynomial Neuron-Based Self-Organizing Neural Networks. Int J Gen Syst 32(3):237–250CrossRefzbMATHGoogle Scholar
  16. 16.
    Richard N, Frank N (2006) On weighted clustering. IEEE Trans Pattern Anal Mach Intell 28:1223–1235CrossRefGoogle Scholar
  17. 17.
    Gentile C, Warmuth M (2000) Proving relative loss bounds for on-line learning algorithm using Bregman divergences. In: Proc. Tutorials 13th Int’l Conf. Computational learning theoryGoogle Scholar
  18. 18.
    Pedrycz W, Izakian H (2014) Cluster-Centric Fuzzy Modeling. IEEE Trans Fuzzy Syst 22(4):1585–1597CrossRefGoogle Scholar
  19. 19.
    Zadeh LA (1997) Toward a Theory of Fuzzy Information Granulation and Its Centrality in Human Reasoning and Fuzzy Logic. Fuzzy Set Syst 90:111–117MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Sanchez L, Couso I, Casillas J (2009) Genetic Learning of Fuzzy Rules Based on Low Quality Data. Fuzzy Set Syst 160(17):2524–2552MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Bezdek JC (1981) Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New YorkCrossRefzbMATHGoogle Scholar
  22. 22.
    Pedrycz W (1984) An Identification Algorithm in Fuzzy Relational System. Fuzzy Set Syst 13:153–167CrossRefzbMATHGoogle Scholar
  23. 23.
    Tong RM (1980) The Evaluation of Fuzzy Models Derived from Experimental Data. Fuzzy Set Syst 13:1–12CrossRefzbMATHGoogle Scholar
  24. 24.
    Xu CW, Zailu Y (1987) Fuzzy Model Identification Self-learning for Dynamic System. IEEE Trans Syst Man Cybern 17(4):683–689CrossRefGoogle Scholar
  25. 25.
    Sugeno M, Yasukawa T (1991) Linguistic Modeling Based on Numerical Data. In: IFSA’91 Brussels, Computer, Management & System Science, pp, 264-267Google Scholar
  26. 26.
    Oh SK, Pedrycz W (2000) Identification of Fuzzy Systems by means of an Auto-Tuning Algorithm and Its Application to Nonlinear Systems. Fuzzy Sets Syst 115(2):205–230MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Park BJ, Pedrycz W, Oh SK (2001) Identification of Fuzzy Models with the Aid of Evolutionary Data Granulation. IEE Proc.-Control Theory and Applications 148:406–418CrossRefGoogle Scholar
  28. 28.
    Park HS, Oh SK, Yoon YW (2001) A New Modeling Approach to Fuzzy-Neural Networks Architecture (in Korea). J Control Automat Syst Eng 7:664–674Google Scholar
  29. 29.
    Oh SK, Pderycz W, Park HS (2006) Genetically Optimized Fuzzy Polynomial Neural Networks. IEEE Trans Fuzzy Syst 14:125–144CrossRefGoogle Scholar
  30. 30.
    Oh S-K, Pedrycz W, Park B-J (2004) Relation-based Neurofuzzy Networks with Evolutionary Data Granulation. Math Comput Model 40(7-8):891–921MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Oh SK, Park HS, Jeong CW, Joo SC (2009) GA-based Feed-forward Self-organizing Neural Network Architecture and Its Applications for Multi-variable Nonlinear Process Systems, vol 3, pp 309–330Google Scholar
  32. 32.
    Oh SK, Pedrycz W (2003) Fuzzy Polynomial Neuron-Based Self-Organizing Neural Networks. Int J Gen Syst 32(3):237–250CrossRefzbMATHGoogle Scholar
  33. 33.
    Choi JN, Oh SK, Pedrycz W (2008) Identification of Fuzzy Models Using a Successive Tuning Method with a Variant Identification Ratio. Fuzzy Sets Syst 159(21):2873–2889MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Pedrycz W, Kwak K-C (2007) The Development of Incremental Models. IEEE Trans Fuzzy Syst 15 (3):507–518CrossRefGoogle Scholar
  35. 35.
    Alcala R, Ducange P, Herrera F, Lazzerini B, Marcelloni F (2009) A Multiobjective Evolutionary Approach to Concurrently Learn Rule and Data Bases of Linguistic Fuzzy-Rule-Based Systems. IEEE Trans Fuzzy Syst 17:1106–1122CrossRefGoogle Scholar
  36. 36.
    Alcala R, Gacto MJ, Herrera F (2011) A Fast and Scalable Multiobjective Genetic Fuzzy System for Linguistic Fuzzy Modeling in High-Dimensional Regression Problems. IEEE Trans Fuzzy Syst 19:666–681CrossRefGoogle Scholar

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

Personalised recommendations