Neuro-fuzzy modelling based on a deterministic annealing approach

• Autorzy: Czabański R.
• Języki publikacji: EN

Abstrakty

EN

This paper introduces a new learning algorithm for artificial neural networks, based on a fuzzy inference system ANBLIR. It is a computationally effective neuro-fuzzy system with parametrized fuzzy sets in the consequent parts of fuzzy if-then rules, which uses a conjunctive as well as a logical interpretation of those rules. In the original approach, the estimation of unknown system parameters was made by means of a combination of both gradient and least-squares methods. The novelty of the learning algorithm consists in the application of a deterministic annealing optimization method. It leads to an improvement in the neuro-fuzzy modelling performance. To show the validity of the introduced method, two examples of application concerning chaotic time series prediction and system identification problems are provided.

Słowa kluczowe

EN

fuzzy systems; neural networks; neuro-fuzzy system; rules extraction; deterministic annealing; prediction

PL

system rozmyty; sieć neuronowa; ekstrakcja reguł

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2005
• Tom: Vol. 15, no 4
• Strony: 561--576
• Opis fizyczny: Bibliogr. 46 poz., tab., wykr.

Twórcy

autor

Czabański R.

• Department of Automatic Control, Electronics and Computer Sciences Silesian University of Technology ul. Akademicka 16, 44–100 Gliwice, 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] 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.
• [4] Cho K.B. and Wang B.H. (1996): Radial basis function based adaptive fuzzy systems and their applications to system identification and prediction. — Fuzzy Sets Syst., Vol. 83, No. 3, pp. 325–339.
• [5] Chung F.L. and Duan J.C. (2000): On multistage fuzzy neural network modeling. — IEEE Trans. Fuzzy Syst., Vol. 8, No. 2, pp. 125–142.
• [6] Czogała E. and Łęski J. (1996): A new fuzzy inference system with moving consequents in if-then rules. Application to pattern recognition. — Bull. Polish Acad. Sci., Vol. 45, No. 4, pp. 643–655.
• [7] Czogała E. and Łęski J. (1999): Fuzzy and Neuro-Fuzzy Intelligent Systems. —Heidelberg: Physica-Verlag.
• [8] Czogała E. and Łęski J. (2001): On equivalence of approximate reasoning results using different interpretations of if-then rules. — Fuzzy Sets Syst., Vol. 117, No. 2, pp. 279–296.
• [9] German S. and German D. (1984): Stochastic relaxation, Gibbs distribution and the Bayesian restoration in images. — IEEE Trans. Pattern Anal. Mach. Intell., Vol. 6, No. 9, pp. 721–741.
• [10] Jang J.S.R. (1993): ANFIS: Adaptive-Network-Based Fuzzy Inference System. — IEEE Trans. Syst. Man Cybern., Vol. 23, No. 3, pp. 665–685.
• [11] Jang J.S.R. and Sun C.T. (1993): Functional equivalence between radial basis function networks and fuzzy inference systems. — IEEE Trans. Neural Netw., Vol. 4, No. 1, pp. 156–159.
• [12] Jang J.S.R. and Sun C.T. (1995): Neuro-fuzzy modeling and control.— Proc. IEEE, Vol. 83, No. 3, pp. 378–406.
• [13] 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.
• [14] Juang C. and Lin C. (1998): An on-line self-constructing neural fuzzy inference network and its applications. — IEEE Trans. Fuzzy Syst., Vol. 6, No. 1, pp. 12–32.
• [15] 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.
• [16] Kirkpatrick S., Gelatt C. and Vecchi M. (1983): Optimization by simulated annealing. — Science, Vol. 220, No. 4598, pp. 671–680.
• [17] Kosko B. (1987): Fuzzy associative memories In: Fuzzy Expert Systems (A. Kandel, Ed.).—Boca Raton: CRC Press.
• [18] Łęski J. (2003): ε –insensitive learning techniques for approximate reasoning systems.—Int. J. Comput. Cognit., Vol. 1, No. 1, pp. 21–77.
• [19] Lin Y. and Cunningham G.A. (1995): A new approach to fuzzy-neural modeling. – IEEE Trans. Fuzzy Syst., Vol. 3, No. 2, pp. 190–197.
• [20] Mamdani E.H. (1974): Applications of fuzzy algorithms for control of simple dynamic plant. — Proc. IEEE, Vol. 121, No. 12, pp. 1585–1588.
• [21] Mamdani E.H. (1976): Advances in the linguistic synthesis of fuzzy controller.—Int. J. Man–Mach. Stud., Vol. 8, No. 6, pp. 669–678.
• [22] Mamdani E.H. (1977): Applications of fuzzy logic to approximate reasoning using linguistic synthesis. — IEEE Trans. Comput., Vol. 26, No. 12, pp. 1182–1191.
• [23] Mamdani E.H. 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.
• [24] Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H. and Teller E. (1953): Equation of state calculation by fast computing machines. — J. Chem. Phys., Vol. 21, No. 6, pp. 1087–1092.
• [25] Mitra S. and Pal S.K. (1995): Fuzzy multi-layer perceptron, inferencing and rule generation. — IEEE Trans. Neural Netw., Vol. 6, No. 1, pp. 51–63.
• [26] Pedrycz W. (1984a): An identification algorithm in fuzzy relational systems. — Fuzzy Sets Syst., Vol. 13, No. 2, pp. 153–167.
• [27] Pedrycz W. (1984b): Identification in fuzzy systems. — IEEE Trans. Syst. Man Cybern., Vol. 14, No. 2, pp. 361–366.
• [28] Rao A.V. and Rose K. (1999): A deterministic annealing approach for parsimonious design of piecewise regression models. — IEEE Trans. Pattern Anal. Mach. Intell., Vol. 21, No. 2, pp. 159–173.
• [29] Rao A.V., Miller D., Rose K. and Gersho A. (1997): Mixture of experts regression modeling by deterministic annealing. —IEEE Trans. Signal Process., Vol. 45, No. 11, pp. 2811–2820.
• [30] Rose K. (1991): Deterministic Annealing, Clustering and Optimization. — Ph.D. Thesis, California Inst. Technol, Pasadena.
• [31] Rose K. (1998): Deterministic annealing for clustering, compression, classification, regression and related optimization problems. — Proc. IEEE, Vol. 86, No. 11, pp. 2210–2239.
• [32] Rose K. (1999): A deterministic annealing approach for parsimonious design of piecewise regression models. — IEEE Trans. Pattern Anal. Mach. Intell., Vol. 21, No. 2, pp. 159–173.
• [33] Rutkowska D. (2001): Neuro–Fuzzy Architectures and Hybrid Learning. — Heidelberg: Physica–Verlag.
• [34] Schuster H.G. (1984): Deterministic Chaos.—Weinheim: VCH Verlagsgesellschaft.
• [35] Sugeno M. and Kang G.T. (1988): Structure identification of fuzzy model.—Fuzzy Sets Syst., Vol. 28, No. 1, pp. 15–33.
• [36] 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.
• [37] Tong R.M. (1980): The evaluation of fuzzy models derived from experimental data. — Fuzzy Sets Syst., Vol. 4, No. 13, pp. 1–12.
• [38] 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.
• [39] 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.
• [40] 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. 4, pp. 683–689.
• [41] Yager R.R. and Filev D.P. (1984): Essentials of Fuzzy Modeling and Control.— New York: Wiley.
• [42] Yen J.,Wang L. and Gillespie C.W. (1998): Improving the interpretability of TSK fuzzy models by combining global learning and local learning.—IEEE Trans. Fuzzy Syst., Vol. 6, No. 4, pp. 530–537.
• [43] Zadeh L.A. (1965): Fuzzy sets. — Inf. Contr., Vol. 8, No. 3, pp. 338–353.
• [44] Zadeh L.A. (1971): Towards a theory of fuzzy systems, In: Aspects of Network and System Theory (R.E. Kalman and N. DeClaris, Ed.).—New York: Holt, Rinehart & Winston.
• [45] 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.
• [46] Zikidis K.C. and Vasilakos A.V. (1996): ASAFES2: A novel, neuro-fuzzy architecture for fuzzy computing, based on functional reasoning. — Fuzzy Sets Syst., Vol. 83, No. 1, pp. 63–68.