Identification of Fuzzy Inference Systems Using a Multi-objective Space Search Algorithm and Information Granulation

  • Huang, Wei (School of Computer and Communication Engineering, Tianjin University of Technology) ;
  • Oh, Sung-Kwun (Dept. of Electrical Engineering, The University of Suwon) ;
  • Ding, Lixin (State Key Laboratory of Software Engineering, Wuhan University) ;
  • Kim, Hyun-Ki (Dept. of Electrical Engineering, The University of Suwon) ;
  • Joo, Su-Chong (Dept. of Computer Engineering, Wonkwang University)
  • Received : 2010.09.07
  • Accepted : 2011.03.11
  • Published : 2011.11.01


We propose a multi-objective space search algorithm (MSSA) and introduce the identification of fuzzy inference systems based on the MSSA and information granulation (IG). The MSSA is a multi-objective optimization algorithm whose search method is associated with the analysis of the solution space. The multi-objective mechanism of MSSA is realized using a non-dominated sorting-based multi-objective strategy. In the identification of the fuzzy inference system, the MSSA is exploited to carry out parametric optimization of the fuzzy model and to achieve its structural optimization. The granulation of information is attained using the C-Means clustering algorithm. The overall optimization of fuzzy inference systems comes in the form of two identification mechanisms: structure identification (such as the number of input variables to be used, a specific subset of input variables, the number of membership functions, and the polynomial type) and parameter identification (viz. the apexes of membership function). The structure identification is developed by the MSSA and C-Means, whereas the parameter identification is realized via the MSSA and least squares method. The evaluation of the performance of the proposed model was conducted using three representative numerical examples such as gas furnace, NOx emission process data, and Mackey-Glass time series. The proposed model was also compared with the quality of some "conventional" fuzzy models encountered in the literature.


Supported by : National Research Foundation of Korea


  1. W. Pedrycz, "An identification algorithm in fuzzy relational system". Fuzzy Sets Syst., vol. 13, pp, 153-167, 1984.
  2. R. M. Tong, "The evaluation of fuzzy models derived from experimental data," Fuzzy Sets Syst., vol. 13, pp 1-12, 1980.
  3. C. W. Xu., Y. Zailu, "Fuzzy model identification selflearning for dynamic system" IEEE Trans. Syst., Man cybern., vol. 17, no 4, pp, 683-689, 1987.
  4. M. Sugeno, T. Yasukawa, "Linguistic modeling based on numerical data." in Proceedings of IFSA'91 Brussels, Computer, Management & System Science, pp, 264-267. 1991.
  5. S. K. Oh., W. Pedrycz, "Identification of Fuzzy Systems by means of an Auto-Tuning Algorithm and Its Application to Nonlinear Systems," Fuzzy Sets and Syst., vol. 115, no 2, pp, 205-230, 2000.
  6. W.Y Chung, W. Pedrycz, E.T Kim, "A new twophase approach to fuzzy modeling for nonlinear function approximation," IEICE Trans. Info. Syst., vol. 9, pp, 2473-2483, 2006.
  7. B. J. Park., W. Pedrycz., S. K. Oh, "Identification of Fuzzy Models with the Aid of Evolutionary Data Granulation". IEE Proc.-Control Theory and Applications, vol. 148, pp, 406-418, 2001.
  8. W.Y. Chung, E.T. Kim, "A new two-phase approach to fuzzy modeling for nonlinear function approximation," IEICE Trans. Inform. Syst., vol. E89-D, no. 9, pp. 2473-2483, 2006.
  9. F.J. Lin, L.T. Teng, J.W. Lin, S.Y. Chen, "Recurrent Functional-Link-Based Fuzzy-Neural-Network-Controlled Induction-Generator System Using Improved Particle Swarm Optimization," IEEE Trans. Indust. Elect., vol. 56, no. 5, pp. 1557-1577, 2009.
  10. W. Pedrycz, K.C Kwak, "Linguistic models as a framework of user-centric system modeling," IEEE Trans. Syst., man cybern. -PART A : Systems and humans, vol. 36, no. 4, pp. 727-745, 2006.
  11. A. Bastian, "Identifying fuzzy models utilizing genetic programming," Fuzzy Sets and Syst., vol. 112, pp. 333-350, 2000.
  12. Y. Jin, "Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement," IEEE Trans. Fuzzy Syst., vol. 8, no. 2, pp. 212-221, 2000.
  13. M. Setnes, H. Roubos, "GA-based modeling and classification: complexity and performance," IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 509-522, 2000.
  14. C. Coello, G. Pulido, "Multiobjective optimization using a micro-genetic algorithm," in Proceedings of Genetic and Evolutionary Computation Conference (GECCO 2001), pp. 274-282, 2001.
  15. K. Deb, S. Agrawal, A. Pratab, S. Agarwal, T. Meyarivan, "A fast and elitist multi-objective genetic algorithm: NSGA-II," IEEE Trans. Evol. Comput. , vol. 6, no.2, pp. 182-197, 2002.
  16. G. Avigad, A. Moshaiov, "Interactive Evolutionary Multiobjective Search and Optimization of Set-Based Concepts," IEEE Trans. Syst., Man cybern.-Part B, vol. 38, nol. 2, pp. 381-403, 2008.
  17. C. Coello, G. Pulido, M. Salazar, "Handling multiobjectives with particle swarm optimization," IEEE Trans. Evol. Comput., vol. 8, pp. 256-279, 2004.
  18. G.G. Yen, W.F. Leong, "Dynamic Multiple Swarms in Multiobjective Particle Swarm Optimization," IEEE Trans. Syst., Man Cybern.-PART A, vol. 39, nol. 4, pp. 890-911, 2009.
  19. L.J. Herrera, H. Pomares, I. Rojas, O. Valenzuela, and A. Prieto, "TaSe, a Taylor series-based fuzzy system model that combines interpretability and accuracy," Fuzzy Sets and Syst., vol. 153, pp. 403-427, 2005.
  20. M. Delgado, M.P. Ceullar, and M.C. Pegalajar, "Multiobjective Hybrid Optimization and Training of Recurrent Neural Networks," IEEE Trans. Syst., Man cybern. -Part B, vol. 38, nol. 2, pp. 381-403, 2008.
  21. W. Huang, L. Ding, "Project-Scheduling problem with random time-dependent activity duration times," IEEE Transactions on Engineering Management, vol. 58, no. 2, pp. 377-387, May 2011.
  22. W. Huang, L. Ding, S.K. Oh, C.W. Jeong, S.C. Joo, "Identification of fuzzy inference system based on information granulation," KSII Transactions on Internet and Information Systems, vol. 4, no. 4, pp. 575-594, August 2010.
  23. B. J. Park., W. Pedrycz., S. K. Oh, "Identification of Fuzzy Models with the Aid of Evolutionary Data Granulation," IEE Proc.-Control Theory and Applications, vol. 148, pp, 406-418, 2001
  24. K.J. Park, W. Pedrycz, S.K. Oh, "A genetic approach to modeling fuzzy systems based on information granulation and successive generation-based evolution method", Simulation Modelling Practice and Theory, vol. 15, pp, 1128-1145, 2007.
  25. S.K. Oh, W. Pedrycz, H.S. Prak, "Hybrid identification in fuzzy-neural networks", Fuzzy Set System, vol. 138, Issue 2, pp, 399-426, 2003.
  26. H.S. Park, S.K. Oh, "Fuzzy relation-based fuzzy neural-networks using a hybrid identification algorithm", Int. J. Cont., Autom., Syst., vol. 1, Issue 2, pp. 289-300, 2003.
  27. H.S. Park, S.K. Oh, "Multi-FNN identification based on HCM clustering and evolutionary fuzzy granulation", Int. J. Cont., Autom., Syst., vol. 1, Issue 2, pp. 194-202, 2003.
  28. S.K. Oh, W. Pedrycz, H.S. Prak, "Implicit rule-based fuzzy-neural networks using the identification algorithm of hybrid scheme based on information granulation", Adv. Eng. Inform. vol. 16, Issue 4, pp. 247-263, 2002.
  29. J.N. Choi, S.K. Oh, W. Pedrycz, "Identification of fuzzy relation models using hierarchical fair competition-based parallel genetic algorithms and information granulation", Applied Mathematical Modelling, vol. 33, pp. 2791-2807, 2009.
  30. In: P.R. Krishnaiah., L.N. Kanal (Eds.), "Classification, Pattern Recognition, and Reduction of Dimensionality", Handbook of Statistics, vol. 2, North-Holland, Amsterdam, 1982.
  31. L. X. Wang., J. M. Mendel, "Generating fuzzy rules from numerical data with applications", IEEE Trans. Syst., man cybern., vol. 22, pp. 1414-1427, 1992.
  32. J.S.R Jang, "ANFIS: adaptive-network-based fuzzy inference system", IEEE Trans. Syst., man cybern., vol. 23, no. 3, pp. 665-685, 1993.
  33. L.P. Maguire, B. Roche, T.M. McGinnity, L.J. McDaid, "Predicting a chaotic time series using a fuzzy neural, network", Inform. Sci., vol. 112, pp. 125-136, 1998.
  34. J.C. Duan., F.-L. Chung, "Multilevel fuzzy relational systems: structure and identification", Soft Comput., vol. 6, pp. 71-86, 2002.
  35. Y. Chen., B. Yang., A. Abraham, "Automatic design of hierarchical Takagi-Sugeno type fuzzy systems using evolutionary algorithms", IEEE Trans. Fuzzy Systems, vol. 15, no. 3, pp. 385-397, 2007.

Cited by

  1. A Novel Fuzzy Identification Method Based on Ant Colony Optimization Algorithm vol.4, 2016,
  2. Multiobjective Space Search Optimization and Information Granulation in the Design of Fuzzy Radial Basis Function Neural Networks vol.7, pp.4, 2012,
  3. Data-Driven Interval Type-2 Neural Fuzzy System With High Learning Accuracy and Improved Model Interpretability vol.43, pp.6, 2013,
  4. A novel identification method for Takagi–Sugeno fuzzy model 2017,
  5. Hierarchical Structured Sparse Representation for T–S Fuzzy Systems Identification vol.21, pp.6, 2013,
  6. Dynamic T-S Fuzzy Systems Identification Based on Sparse Regularization vol.17, pp.1, 2015,
  7. Design of Fuzzy Models with the Aid of an Improved Differential Evolution vol.22, pp.4, 2012,
  8. Joint Block Structure Sparse Representation for Multi-Input–Multi-Output (MIMO) T–S Fuzzy System Identification vol.22, pp.6, 2014,
  9. Identification of Fuzzy Inference Systems by Means of a Multiobjective Opposition-Based Space Search Algorithm vol.2013, 2013,
  10. Design of Reinforced Interval Type-2 Fuzzy C-Means-Based Fuzzy Classifier vol.26, pp.5, 2018,
  11. Hybrid Fuzzy Wavelet Neural Networks Architecture Based on Polynomial Neural Networks and Fuzzy Set/Relation Inference-Based Wavelet Neurons vol.29, pp.8, 2018,