A Fuzzy System with ε-insensitive Learning of Premises and Consequences of if-then Rules

• Autorzy: Łęski J. M. , Czogała T.
• Języki publikacji: EN

Abstrakty

EN

First, a fuzzy system based on if-then rules and with parametric consequences is recalled. Then, it is shown that the global and local ε-insensitive learning of the above fuzzy system may be presented as a combination of both an ε-insensitive gradient method and solving a system of linear inequalities. Examples are given of using the introduced method to design fuzzy models of real-life data. Simulation results show an improvement in the generalization ability of a fuzzy system trained by the new method compared with the traditional and other ε-insensitive learning methods.

Słowa kluczowe

EN

fuzzy system; generalization ability; extraction of fuzzy if-then rules; global ε-insensitive learning; local ε-insensitive learning

PL

system rozmyty; zdolność uogólnienia; modelowanie rozmyte

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2005
• Tom: Vol. 15, no 2
• Strony: 257--273
• Opis fizyczny: Bibliogr. 36 poz., tab., wykr.

Twórcy

autor

Łęski J. M.

• Institute of Electronics, Silesian University of Technology, ul. Akademicka 16, 44–100 Gliwice, Poland

autor

Czogała T.

• Institute of Medical Technology and Equipment, ul. Roosevelta 118A, 41–800 Zabrze, Poland

Bibliografia

• [1] Bezdek J.C. (1982): Pattern Recognition with Fuzzy Objective Function Algorithms. —New York: Plenum Press.
• [2] Box G.E.P. and Jenkins G.M. (1976): Time Series Analysis. Forecasting and Control.— San Francisco: Holden-Day.
• [3] Castellano G., Fanelli A.M. and Mencor C. (2004): An empirical risk functional to improve learning in a neuro-fuzzy classifier. — IEEE Trans. Sys. Man Cybern., Part B: Cybernetics, Vol. 34, No. 1, pp. 725–730.
• [4] Chen J.-Q., Xi Y.-G. and Zhang Z.-J. (1998): A clustering algorithm for fuzzy model identification. — Fuzzy Sets Syst., Vol. 98, No. 2, pp. 319–329.
• [5] Chen J.-H. and Chen C.-S. (2002): Fuzzy kernel perceptron. — IEEE Trans. Neural Netw., Vol. 13, No. 6, pp. 1364–1373.
• [6] Chiang J.-H. and Hao P.-Y. (2003): A new kernel-based fuzzy clustering approach: support vector clustering with cell growing. — IEEE Trans. Fuzzy Syst., Vol. 11, No. 4, pp. 518–527.
• [7] Czogała E. and Łęski J.M. (2000): Fuzzy and Neuro-Fuzzy Intelligent Systems. —Heidelberg: Physica-Verlag.
• [8] Czogała E. and Łęski J.M. (2001): On equivalence of approximate reasoning results using different interpretations of fuzzy if-then rules. — Fuzzy Sets Syst., Vol. 117, No. 2, pp. 279–296.
• [9] Ho Y.-C. and Kashyap R.L. (1965): An algorithm for linear inequalities and its applications. — IEEE Trans. Elec. Comp., Vol. 14, No. 5, pp. 683–688.
• [10] Ho Y.-C. and Kashyap R.L. (1966): A class of iterative procedures for linear inequalities. — SIAM J. Contr., Vol. 4, No. 2, pp. 112–115.
• [11] Hong D.H. and Hwang C. (2003): Support vector fuzzy regression machines. — Fuzzy Sets Syst., Vol. 138, No. 2, pp. 271–281.
• [12] Jang J.-S.R., Sun C.-T. and Mizutani E. (1997): Neuro-fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence. — Upper Saddle River: Prentice-Hall.
• [13] Jeng J.-T., Chuang C.-C. and Su S.-F. (2003): Support vector interval regression networks for interval regression analysis. — Fuzzy Sets Syst., Vol. 138, No. 2, pp. 283–300.
• [14] Lin C.-F. and Wang S.-D. (2002): Fuzzy support vector machine. —IEEE Trans. Neural Netw., Vol. 13, No. 2, pp. 464–471.
• [15] Łęski J.M. and Czogała E. (1999): A new artificial neural network based fuzzy inference system with moving consequents in if-then rules and its applications. — Fuzzy Sets Syst., Vol. 108, No. 3, pp. 289–297.
• [16] Łęski J.M. (2001): An ε-insensitive approach to fuzzy clustering. — Int. J. App. Math. Comp. Sci., Vol. 11, No. 4, pp. 993–1007.
• [17] Łęski J.M. (2001): Neuro-fuzzy modeling with ε-insensitive learning. — Methods of Artificial Intelligence in Mechanics and Mechanical Engineering, Gliwice, Poland, pp. 133–138.
• [18] Łęski J.M. (2002a): ε-insensitive learning techniques for approximate reasoning systems (Invited Paper). — Int. J. Comp. Cognition, Vol. 1, No. 1, pp. 21–77.
• [19] Łęski J.M. (2002b): Improving generalization ability of neurofuzzy system by ε-insensitive learning. — Int. J. Appl. Math. Comp. Sci., Vol. 12, No. 3, pp. 437–447.
• [20] Łęski J.M. (2003a): Towards a robust fuzzy clustering.—Fuzzy Sets Syst., Vol. 137, No. 2, pp. 215–233.
• [21] Łęski J.M. (2003b): Neuro-fuzzy system with learning tolerant to imprecision.—Fuzzy Sets Syst., Vol. 138, No. 2, pp. 427–439.
• [22] Łęski J.M. (2004a): ε-insensitive fuzzy -regression models: Introduction to ε-insensitive fuzzy modeling. — IEEE Trans. Syst. Man Cybern., Part B: Cybernetics, Vol. 34, No. 1, pp. 4–15.
• [23] Łęski J.M. (2004b): An ε-margin nonlinear classifier based on if-then rules. — IEEE Trans. Syst. Man Cybern., Part B: Cybernetics, Vol. 34, No. 1, pp. 68–76.
• [24] Mendel J.M. (1983): Optimal Seismic Deconvolution. An Estimation-Based Approach. — New York: Academic Press.
• [25] Pedrycz W. (1984): An identification algorithm in fuzzy relational systems. — Fuzzy Sets Syst., Vol. 13, No. 1, pp. 153–167.
• [26] Rutkowska D. (2001): Neuro-Fuzzy Architectures and Hybrid Learning. — Heidelberg: Physica-Verlag.
• [27] Rutkowski L. and Cpalka K. (2003): Flexible neuro-fuzzy systems. — IEEE Trans. Neural Netw., Vol. 14, No. 3, pp. 554–574.
• [28] Setnes M. (2000): Supervised fuzzy clustering for rule extraction. — IEEE Trans. Fuzzy Syst., Vol. 8, No. 4, pp. 416–424.
• [29] 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.
• [30] Tong R.M. (1980): The evaluation of fuzzy models derived from experimental data. — Fuzzy Sets Syst., Vol. 4, No. 1, pp. 1–12.
• [31] Vapnik V. (1995): The Nature of Statistical Learning Theory. — New York: Springer.
• [32] Vapnik V. (1998): Statistical Learning Theory. — New York: Wiley.
• [33] Vapnik V. (1999): An overview of statistical learning theory. — IEEE Trans. Neural Netw., Vol. 10, No. 5, pp. 988–999.
• [34] Xie X.L. and Beni G. (1991): A validity measure for fuzzy clustering.— IEEE Trans. Pattern Anal. Mach. Intell., Vol. 13, No. 8, pp. 841–847.
• [35] Xu C.W. and Lu Y.Z. (1987): Fuzzy model identification and self-learning for dynamic systems. — IEEE Trans. Syst., Man Cybern., Vol. 17, No. 3, pp. 190–197.
• [36] Zadeh L. A. (1973): Outline of a new approach to the analysis of complex systems and decision processes.—IEEE Trans. Syst. Man Cybern., Vol. 3, No. 1, pp. 28–44.