×

zbMATH — the first resource for mathematics

Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks. (English) Zbl 0964.62051
Summary: In this paper, first we explain several versions of fuzzy regression methods based on linear fuzzy models with symmetric triangular fuzzy coefficients. Next we point out some limitations of such fuzzy regression methods. Then we extend the symmetric triangular fuzzy coefficients to asymmetric triangular and trapezoidal fuzzy numbers. We show that the limitations of the fuzzy regression methods with the symmetric triangular fuzzy coefficients are remedied by such extension. Several formulations of linear programming problems are proposed for determining asymmetric fuzzy coefficients from numerical data. Finally, we show how fuzzified neural networks can be utilized as nonlinear fuzzy models in fuzzy regression.
In the fuzzified neural networks, asymmetric fuzzy numbers are used as connection weights. The fuzzy connection weights of the fuzzified neural networks correspond to the fuzzy coefficients of the linear fuzzy models. Nonlinear fuzzy regression based on the fuzzified neural networks is illustrated by computer simulations where Type I and Type II membership functions are determined from numerical data.

MSC:
62J86 Fuzziness, and linear inference and regression
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alefeld, G.; Herzberger, J., Introduction to interval computations, (1983), Academic Press New York
[2] Buckley, J.J.; Hayashi, Y., Fuzzy neural networks: a survey, Fuzzy sets and systems, 66, 1, 1-13, (1994)
[3] J. Dunyak, D. Wunsch, A training technique for fuzzy number neural networks, Proc. 1997 IEEE Internat. Conf. on Neural Networks, 1997, pp. 533-536.
[4] T. Feuring, Learning in fuzzy neural networks, Proc. 1996 IEEE Internat. Conf. on Neural Networks, 1996, pp. 1061-1066.
[5] Hayashi, Y.; Buckley, J.J.; Czogala, E., Fuzzy neural network with fuzzy signals and weights, Internat. J. intelligent systems, 8, 527-537, (1993) · Zbl 0938.68787
[6] Ishibuchi, H.; Fujioka, R.; Tanaka, H., Neural networks that learn from fuzzy if – then rules, IEEE trans. fuzzy systems, 1, 2, 85-97, (1993)
[7] Ishibuchi, H.; Morioka, K.; Turksen, I.B., Learning by fuzzified neural networks, Internat. J. approx. reasoning, 13, 4, 327-358, (1995) · Zbl 0956.68527
[8] Ishibuchi, H.; Tanaka, H., Interval regression analysis by mixed 0-1 integer programming problem, J. jpn. indust. management assoc, 40, 5, 312-319, (1989), (in Japanese)
[9] Ishibuchi, H.; Tanaka, H., Fuzzy regression analysis using neural networks, Fuzzy sets and systems, 50, 3, 257-266, (1992)
[10] Ishibuchi, H.; Tanaka, H.; Okada, H., Interpolation of fuzzy if – then rules by neural networks, Internat. J. approx. reasoning, 10, 1, 3-27, (1994) · Zbl 0794.68133
[11] Kaufmann, A.; Gupta, M.M., Introduction to fuzzy arithmetic, (1985), Van Nostrand Reinhold New York · Zbl 0588.94023
[12] P.V. Krishnamraju, J.J. Buckley, K.D. Reilly, Y. Hayashi, Genetic learning algorithms for fuzzy neural nets, Proc. 1994 IEEE Internat. Conf. on Fuzzy Systems, 1994, pp. 1969-1974.
[13] A. Miyazaki, K. Kwon, H. Ishibuchi, H. Tanaka, Fuzzy regression analysis by fuzzy neural networks and its application, Proc. 1994 IEEE Internat. Conf. on Fuzzy Systems, 1994, pp. 52-57.
[14] D.E. Rumelhart, J.L. McClelland and the PDP Research Group, Parallel Distributed Processing, MIT Press, Cambridge, MA, 1986.
[15] Tanaka, H.; Hayashi, I.; Watada, J., Possibilistic linear regression analysis for fuzzy data, Eur. J. oper. res., 40, 3, 389-396, (1989) · Zbl 0669.62054
[16] Tanaka, H.; Ishibuchi, H., Possibilistic regression analysis based on linear programming, (), 47-60
[17] Tanaka, H.; Ishibuchi, H., Seung gook hwang, fuzzy model of the number of staff in local government by fuzzy regression analysis with similarity relations, J. jpn. indust. management assoc., 41, 2, 99-104, (1990), (in Japanese)
[18] Tanaka, H.; Uejima, S.; Asai, K., Linear regression analysis with fuzzy model, IEEE trans. systems man cybernet., 12, 6, 903-907, (1982) · Zbl 0501.90060
[19] H.N. Teodorescu, D. Arotaritei, Analysis of learning algorithms performance for algebraic fuzzy neural networks, Proc. 1997 Internat. Fuzzy Systems Association World Congress, Vol. IV, 1997, pp. 468-473.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.