Evolution-fuzzy rule based system with parameterized consequences

Czekalski, Piotr

International Journal of Applied Mathematics and Computer Science, Tome 16 (2006), p. 373-385 / Harvested from The Polish Digital Mathematics Library

Résumé

While using automated learning methods, the lack of accuracy and poor knowledge generalization are both typical problems for a rule-based system obtained on a given data set. This paper introduces a new method capable of generating an accurate rule-based fuzzy inference system with parameterized consequences using an automated, off-line learning process based on multi-phase evolutionary computing and a training data covering algorithm. The presented method consists of the following steps: obtaining an initial set of rules with parameterized consequences using the Michigan approach combined with an evolutionary strategy and a covering algorithm for the training data set; reducing the obtained rule base using a simple genetic algorithm; multi-phase tuning of the fuzzy inference system with parameterized consequences using the Pittsburgh approach and an evolutionary strategy. The paper presents experimental results using popular benchmark data sets regarding system identification and time series prediction, providing a reliable comparison to other learning methods, particularly those based on neuro-fuzzy, clustering and ε-insensitive methods. An examplary fuzzy inference system with parameterized consequences using the Reichenbach implication and the minimum t-norm was implemented to obtain numerical results. sm

Détail

Publié le : 2006-01-01

Zbl 1144.68339

EUDML-ID : urn:eudml:doc:207800

Bibliographie

[000] Angelov P. (2002): Evolving Rule-Based Models. A Tool for Design of Flexible Adaptive Systems. - Wurzburg: Physica-Verlag. | Zbl 1043.93001

[001] Arabas J. (2001): Lectures on Evolutionary Algorithms. - Warsaw: Wydawnictwa Naukowo-Techniczne, (in Polish).

[002] Baron L., Achiche S. and Balazinski M. (2001): Fuzzy decision support system knowledge base generation using a genetic algorithm. - Int. J. Approx. Reason., Vol. 1, No. 28, pp. 125-148. | Zbl 0991.68089

[003] Bezdek J. (1981): Pattern Recognition with Fuzzy Objective Function Algorithms. - New York: Plenum Press. | Zbl 0503.68069

[004] Bonarini A. (1996): Evolutionary learning of fuzzy rules: Competition and cooperation, In: Fuzzy Modelling: Paradigms and Practice (W. Pedrycz, Ed.). - Norwell: Kluwer. | Zbl 0881.68098

[005] Box G. and Jenkins G. (1976): Time Series Analysis. Forecasting and Control. - San Francisco: Holden-Day. | Zbl 0363.62069

[006] Carse B., Fogarty T.C. and Munro A. (1996): Evolving fuzzy rule based controllers using genetic algorithms. - Fuzzy Sets Syst., Vol. 80, No. 3, pp. 273-294.

[007] Chen J.Q., Xi Y.G. and Zhang Z.J. (1998): A clustering algorithm for fuzzy model identification. - Fuzzy Sets Syst., Vol. 98,No. 3, pp. 319-329.

[008] Cordon O. and Herrera F. (1997a): Identification of linguistic fuzzy models by means of genetic algorithms, In: Fuzzy Model Identification. Selected Approaches (D. Driankow and H. Hellendoorn, Eds.). - Berlin: Springer. | Zbl 0899.93008

[009] Cordon O. and Herrera F. (1997b): A three-stage evolutionary process for learning descriptive and approximative fuzzy logic controller knowledge bases from examples. - Int. J. Approx. Reason., Vol. 17, No. 4, pp. 369-407. | Zbl 1078.93541

[010] Cordon O. and Herrera F. (2001): Hybridizing genetic algorithms with sharing scheme and evolution strategies for designing approximate fuzzy rule-based systems. - Fuzzy Sets Syst., Vol. 118, No. 2, pp. 235-255. | Zbl 0985.68049

[011] Cordon O., Del Jesus M., Herrera F. and Lozano M. (1999): MOGUL: A methodology to obtain genetic fuzzy rule-based systems under the iterative rule learning approach. - Int. J. Intell. Syst., Vol. 14, No. 11, pp. 1123-1153. | Zbl 0941.68750

[012] Cordon O., Herrera F., Hoffmann F. and Magdalena L. (2001): Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy Knowledge Bases. - Singapore: World Scientific. | Zbl 1042.68098

[013] Cordon O., Gomide F., Herrera F., Hoffmann F. and Magdalena L. (2004): Ten years of genetic fuzzy systems: Current framework and new trends. - Fuzzy Sets Syst., Vol. 141, No. 1, pp. 5-31. | Zbl 1050.93513

[014] Czogala E. and Łęski J. (1996): A new fuzzy inference system with moving consequent in if-then rules. Application to pattern recognition. - J. Bull. Polish Acad. Sci., Vol. 45, No. 4, pp. 643-655. | Zbl 0954.68133

[015] Czogala E. and Łęski J. (1999): Fuzzy and Neuro-Fuzzy Intelligent Systems. - Heidelberg: Physica-Verlag. | Zbl 0953.68122

[016] Fuller R. (1999): Introduction to Neuro-Fuzzy Systems. - Wurzburg: Physica-Verlag. | Zbl 0937.68098

[017] Gonzalez A. and Perez R. (1999): SLAVE: A genetic learning system based on an iterative approach. - IEEE Trans. Fuzzy Syst., Vol. 7, No. 2, pp. 176-191.

[018] Herrera F. and Verdegay J. (1996): Genetic Algorithms and Soft Computing. - Wurzburg: Physica-Verlag. | Zbl 0870.68019

[019] Herrera F., Lozano M. and Verdegay J.L. (1995): Tuning fuzzy logiccontrollers by genetic algorithms. - Int. J. Approx. Reason., Vol. 12, No. 3, pp. 299-315. | Zbl 0875.93242

[020] Hoffmann F. and Pfister G. (1997): Evolutionary design of a fuzzy knowledge base for a mobile robot. - Int. J. Approx. Reason., Vol. 17, No. 4, pp. 447-469. | Zbl 1078.93543

[021] Holland J. (1975): Adaptation in Natural and Artificial Systems. - University of Michigan Press, Ann Arbor.

[022] Holland J. and Reitman J. (1978): Cognitive systems based on adaptive algorithms, In: Pattern-Directed Inference Systems (D.A. Waterman and F. Hayes-Roth, Eds.). - New York: Academic Press.

[023] Ishibuchi H., Nakashima T. and Murata T. (1999): Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems. - IEEE Trans. Syst. Man Cybern., Vol. 29, No. 5, pp. 601-618.

[024] Kim E., Park M. and Ji S. (1997): A new approach to fuzzy modeling. - IEEE Trans. Fuzzy Syst., Vol. 5, No. 3, pp. 328-337.

[025] Lee M.A. and Takagi H. (1993): Integrating design stages of fuzzy systems using genetic algorithms. - Proc. 2nd IEEE Int. Conf. s Fuzzy Systems, San Francisco, CA, pp. 613-617.

[026] Łęski J. (2005): TSK-fuzzy modeling based on ε-insensitive learning. - IEEE Trans. Fuzzy Syst., Vol. 13, No. 2, pp. 181-193.

[027] Łęski J. (2006): Neuro-Fuzzy Systems. - Warsaw: Wydawnictwa Naukowo-Techniczne, (in Polish). | Zbl 0953.68122

[028] Łęski J. and Czogala E. (1999): A new artifficial neural network based fuzzy inference system with moving consequents in if-then rules and selected applications. - Fuzzy Sets Syst., Vol. 108, No. 3, pp. 289-297. | Zbl 0942.93022

[029] Lin Y. and Cunningham H. (1995): A new approach to fuzzy-neural modeling. - IEEE Trans. Fuzzy Syst., Vol. 3, No. 2, pp. 190-197.

[030] Magdalena L. and Monasterio F. (1997): A Fuzzy logic controller with learning through the evolution of its knowledge base. - Int. J. Approx. Reason., Vol. 16, Nos. 3-4, pp. 335-358. | Zbl 0947.93513

[031] Mamdani E. and Assilian S. (1975): An experiment in linguistic synthesis with a fuzzy logic controller. - Int. J. Man-Mach. Stud., Vol. 7, No. 1, pp. 1-13. | Zbl 0301.68076

[032] Michalewicz Z. (2003): Genetic Algorithms + Data Structures = Evolution Programs. - Warsaw: Wydawnictwa Naukowo-Techniczne, (in Polish). | Zbl 0841.68047

[033] Park D., Kandel A. and Langholz G. (1994): Genetic-based new fuzzy reasoning models with application to fuzzy control. - IEEE Trans. Syst. Man Cybern., Vol. 24, No. 1,linebreak pp. 39-47. | Zbl 0850.93452

[034] Parodi A. and Bonelli P. (1993): A new approach to fuzzy classifier systems. - Proc. 5-th Int. Conf. s Genetic Algorithms, Los Altos, pp. 223-230.

[035] Pedrycz W. (1984): An identification algorithm in fuzzy relational systems. - Fuzzy Sets Syst., Vol. 13, No. 2, pp. 153-167. | Zbl 0554.93070

[036] Pedrycz W. (1997): Fuzzy Evolutionary Computation. - Dordrecht: Kluwer. | Zbl 0869.00012

[037] Pham D. and Karaboga D. (1991): Optimum design of fuzzy logic controllers using genetic algorithms. - J. Syst. Eng., Vol. 1, No. 2, pp. 114-118.

[038] Sugeno M. and Kang G. (1988): Structure identification of fuzzy model. - Fuzzy Sets Syst., Vol. 28, No. 1, pp. 15-33. | Zbl 0652.93010

[039] Sugeno M. and Yasukawa T. (1993): A fuzzy-logic based approach to qualitative modeling. - IEEE Trans. Fuzzy Syst., Vol. 1, No. 1, pp. 7-31.

[040] Tadeusiewicz R. (1998): Fundamental introduction to neural neworks techniques with sample implementations. - Warsaw: Akademicka Oficyna Wydawnicza PLJ, (in Polish).

[041] Takagi T. and Sugeno M. (1985): Fuzzy identification of systems and its application to modelling and control. - IEEE Trans. Syst. Man Cybern., Vol. 15, No. 1, pp. 116-132. | Zbl 0576.93021

[042] Thrift P. (1991): Fuzzy logic synthesis with genetic algorithms. - Proc. 4-th Int. Conf. s Genetic Algorithms, Los Altos, pp. 509-513.

[043] Tong R. (1980): The evaluation of fuzzy models derived from experimental data. - Fuzzy Sets Syst., Vol. 4, pp. 1-12. | Zbl 0453.93003

[044] Valenzuela-Rendon M. (1991): The fuzzy classifier system: Motivations and first results. - Proc. 1-st Int. Conf. Parallel Problem Solving from Nature, Berlin, pp. 330-334.

[045] Velasco J. (1998): Genetic-based on-line learning for fuzzy process control. - Int. J. Intell. Syst., Vol. 13, Nos. 10-11, pp. 891-903.

[046] Wang L. and Langari R. (1995): Building Sugeno-type models using fuzzy discretization and orthogonal parameter estimation techniques. - IEEE Trans. Fuzzy Syst., Vol. 3, No. 4, pp. 454-458.

[047] Weigend A., Huberman B. and Rumelhart D. (1990): Predicting the future: A connectionist approach. - Int. J. Neural Syst., Vol. 1, No. 3, pp. 193-209.

[048] Xu C. and Lu Y. (1987): Fuzzy modeling identification and self-learining for dynamic systems. - IEEE Trans. Syst. Man Cybern., Vol. 17, No. 4, pp. 683-689. | Zbl 0643.93018

[049] Zadeh L. (1971): Towards a theory of fuzzy systems, In: Aspects of Network and System Theory (R.E. Kalman and N. De Claris, Eds.). - New York: Holt, Rinehart and Winston.

[050] Zikidis K. and Vasilakos A. (1996): ASAFES2: A novel, neuro-fuzzy architecture for fuzzy computing, based on functional reasoning. - Fuzzy Sets Syst., Vol. 83, No. 1, pp. 63-68.