Abstract
This paper proposes a genetic-based algorithm for generating simple and well-defined Takagi-Sugeno-Kang (TSK) models. The method handles several attributes simultaneously, such as the input partition, feature selection and estimation of the consequent parameters. The model building process comprises three stages. In stage one, structure learning is formulated as an objective weighting optimization problem. Apart from the mean square error (MSE) and the number of rules, three additional criteria are introduced in the fitness function for measuring the quality of the partitions. Optimization of these measures leads to models with representative rules, small overlapping and efficient data cover. To obtain models with good local interpretation, the consequent parameters are determined using a local MSE function while the overall model is evaluated on the basis of a global MSE function. The initial model is simplified at stage two using a rule base simplification routine. Similar fuzzy sets are merged and the “don’t care” premises are recognized. Finally, the simplified models are fine-tuned at stage three to improve the model performance. The suggested method is used to generate TSK models with crisp and polynomial consequents for two benchmark classification problems, the iris and the wine data. Simulation results reveal the effectiveness of our method. The resulting models exhibit simple structure, interpretability and superior recognition rates compared to other methods of the literature.
Similar content being viewed by others
References
Bezdek J (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York
Chiu S (1994) Fuzzy model identification based on cluster estimation. J Intell Fuzzy Syst 2:267–278
Su M-C, Chang H-T (2000) Application of neural networks incorporated with real-valued genetic algorithms in knowledge acquisition. Fuzzy Sets Syst 112:85–97
Chung I-F, Lin C-J, Lin C-T (2000) A GA-based fuzzy adaptive learning control network. Fuzzy Sets Syst 112:65–84
Corcoran AL, Sen S (1994) Using real-valued genetic algorithms to evolve rule sets for classification. In: Proceedings of the 1st IEEE Conference Evolutionary Computation, Orlland, FL, June 1994, pp. 120–124
Cordon O, Herrera F (1999) A two-stage evolutionary process for designing TSK fuzzy rule-based systems. IEEE Trans Syst Man Cybern B 29(6):703–715
Farag WA, Quintana VH, Lambert-Torres G (1998) A genetic-based neuro-fuzzy approach for modeling and control of dynamical systems. IEEE Trans. Neural Netw 9(5):756–767
Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading, MA
Goodwin GC, Sin KS (1984) Adaptive filtering prediction and control. Prentice-Hall, New Jersey
Horikawa S, Furuhashi T, Uchikawa Y (1992) On fuzzy modeling using fuzzy neural networks with back-propagation algorithm. IEEE Trans Neural Netw 3(5):801–806
Hofmaifar A, McCormick E (1995) Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms. IEEE Trans Fuzzy Syst 3(2):129–139
Hoffmann F, Pfister G (1994) Automatic design of hierarchical fuzzy controllers using genetic algorithms. In: Proceeding of Second Conference on Intelligent Techniques and Soft Computing (EUFIT’94), Aachen, Germany, pp.1516–1522
Ishibushi H, Nozaki K, Yamamoto N, Tanaka H (1995) Selecting fuzzy if-then rules for classification problems using genetic algorithms. IEEE Trans Fuzzy Syst 3:260–270
Ishibuchi H, Nakashima T (1999) Voting in fuzzy rule based systems for pattern classification problems. Fuzzy Sets Syst 103:223–238
Ishibuchi H, Nakashima T, Murata T (1999) Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems. IEEE Trans Syst Man Cybern B 29:601–618
Ishigami H, Fukuda T, Shibata T, Arai F (1995) Structure optimization of fuzzy neural network by genetic algorithm. Fuzzy Sets Syst 71:257–264
Jang J-SR (1993) ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23:665–685
Karr CL, Gentry EJ (1993) Fuzzy control of pH using genetic algorithms. IEEE Trans Fuzzy Syst 1:46–53
Kazarlis SA, Papadakis SE, Theocharis JB, Petridis V (2001) Micro-genetic algorithms as generalized hill-climbing operators for GA-optimization. IEEE Trans Evolutionary Comput 5(3):204–217
Kim E, Park M, Ji S, Park M (1997) A new approach to fuzzy modeling. IEEE Trans Fuzzy Syst 2(3):328–337
Lee MA, Takagi H (1993) Integrating design stages of fuzzy systems using genetic algorithms. In: Proceedings of IEEE Int Conf Fuzzy Systems San Fransisco 1:612–617
Lee HM (1998) A neural network classifier with disjunctive fuzzy information. Neural Netw 11(6):1113–1125
Lee HM, Chen CM, Chen JM, You YL (2001) An efficient fuzzy classifier with feature selection based on fuzzy entropy. IEEE Trans Syst Man Cybern B 31:426–432
Liska J, Melsheimer SS (1994) Complete design of fuzzy logic systems using genetic algorithms. Third IEEE Conf Fuzzy Syst 3:1377–1382
Mamdani E (1976) Advances in the linguistic synthesis of fuzzy controllers. Int J Man-Machine Studies 8:669–678
Papadakis SE, Theocharis JB (2002) A GA-based fuzzy modeling approach for generating TSK models. Fuzzy sets and Syst 131:121–152
Setnes M, Roubos H (2000) GA-Fuzzy Modeling and Classification: Complexity and Performance. IEEE Trans Fuzzy Syst 8(5):509–522
Shi Y, Eberhart R, Chen Y (1999) Implementation of evolutionary fuzzy systems. IEEE Trans Syst Man Cybern 7:109–119
Shimojima K, Fukuda T, Hasegawa Y (1995) Self-tuning fuzzy modeling with adaptive membership function, rules, and hierarchical structure based on genetic algorithms. Fuzzy Sets Syst 71:295–309
Simpson PK (1992) Fuzzy min-max neural networks-Part I: Classification. IEEE Trans Neural Netw 3:776–786
Sugeno M, Tanaka K (1991) Successive identification of a fuzzy model and its application to prediction of a complex system. Fuzzy Sets Syst 42:315–334
Sugeno M, Yasukawa T (1993) A fuzzy-logic-based approach to qualitative modeling. IEEE Trans Fuzzy Syst 1(1):7–31
Tamaki H, Kita H, Kabayashi S (1996) Multi-objective optimization by genetic algorithms: A review. IEEE Int Conference on Evolutionary Computing (ICEC’96), 1996, pp 517–522
Tanaka K, Sano M, Watanabe H (1995) Modeling and control of carbon Monoxide concentration using a neuro-fuzzy technique. IEEE Trans Fuzzy Syst 3(3):271–279
Tautz W (1994) Genetic algorithms for designing fuzzy systems. Proceeding of Second Conference on Intelligent Techniques and Soft Computing (EUFIT’94), Aachen, Germany, 1994, pp 558–567
Thrift P (1991) Fuzzy logic synthesis with genetic algorithms. Proceeding of Fourth International Conference on Genetic Algorithms (ICGA’91), 1991, pp 509–513
Wang L, Langari R (1995) Building Sugeno-type models using fuzzy discretization and orthogonal parameter estimation techniques. IEEE Trans Fuzzy Syst 3(4):454–458
Wang L, Langari R (1996) Complex systems modeling via fuzzy logic. IEEE Trans Syst Man Cybern 26:100–106
Wu TP, Chen SM (1999) A new method for constructing membership functions and fuzzy ru, 1999. les from training examples. IEEE Trans Syst Man Cybern B 29:25–40
Wang J-S, Lee CSG (2002) Self-adaptive neuro-fuzzy inference systems for classification applications. IEEE Trans Fuzzy Syst 10(6):790–802
Yager R, Filev D (1993) Unified structure and parameter identification of fuzzy models. IEEE Trans Syst Man Cybern 23(4):1198–1205
Yen J, Wang L, Gillespie CW (1998) Improving the interpretability of TSK fuzzy models by combining global learning and local leaning. IEEE Trans Fuzzy Syst 6(4):530–537
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Papadakis, S.E., Theocharis, J.B. A genetic method for designing TSK models based on objective weighting: application to classification problems.. Soft Comput 10, 805–824 (2006). https://doi.org/10.1007/s00500-005-0010-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-005-0010-1