[논문]Fuzzy regression using regularlization method based on Tanaka's model

Hong Dug-Hun; Kim Kyung-Tae

doi:10.5391/jkiis.2006.16.4.499

Fuzzy regression using regularlization method based on Tanaka's model 원문보기

퍼지 및 지능시스템학회 논문지 = Journal of fuzzy logic and intelligent systems, v.16 no.4, 2006년, pp.499 - 505

Hong Dug-Hun (Department of Mathematics, Myongji University) , Kim Kyung-Tae (Department of Electronics and Electrical Information Engineering, Kyungwon University)

Abstract ▼ AI-Helper

Regularlization approach to regression can be easily found in Statistics and Information Science literature. The technique of regularlization was introduced as a way of controlling the smoothness properties of regression function. In this paper, we have presented a new method to evaluate linear and non-linear fuzzy regression model based on Tanaka's model using the idea of regularlization technique. Especially this method is a very attractive approach to model non -linear fuzzy data.

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가설 설정

Using the data in Table 1, the obtained results from Tanaka's model and our model with h = 0.5 and L(x) = 1 — x are 아lown in Table 2. In this example for our model, C= 500 is used but it heu ristically determined. In fact, the values ot C> 500 give almost same results.

제안 방법

However, some papers, for example [2, 3, 6], were concerned with the data set with fuzzy in puts and fuzzy output. By the way, in this paper we will treat fuzzy nonlinear regression for data of the form with crisp inputs and fuzzy output.
In this paper we will modify this idea for the purpose of deriving the convex optimization problems for fuzzy multiple linear regression models and fuzzy nonlinear regression model with numerical inputs. We now briefly review the Tanaka's model[18].
In this paper, we have presented a new method to evaluate fuzzy linear and fuzzy non-linear regression models based on Tanaka's approach using the idea of regularlization technique. From the results in examples we realize that the derived fuzzy regression models de rive the satisfying solutions and is a very attractive ap proach to modeling fuzzy date, especially for fuzzy non-linear regression model.

이론/모형

In this paper, we will present a new method to eval uate fuzzy regression model based on Tanaka's model using the idea of regularlization method.

참고문헌 (20)

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A. Celmins, A practical approach to nonlinear fuzzy regression, SLAM J. Sci. Stat. Comput., Vol. 12 No. 3 (1991) 521-546

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P. Diamond, Fuzzy least squares, Inform. Sci. 46 (1988) 141-157

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B. Heshmaty, A. Kandel, Fuzzy linear regression and its applications to forecasting in uncertain environment, Fuzzy Sets and Systems 15 (1985) 159-191

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D. Dubois and H. Prade, Theory and Applications, Fuzzy Sets and Systems, Academic Press, New York, 1980
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H. Tanaka, Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems 24 (1987) 363-375

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v H. Tanaka, S. Uejima and K. Asia, Linear regression analysis with Fuzzy model, IEEE Trans. Man. Cybernet. 12 (6) (1982) 903-907

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H. Tanaka, J. Watada, Possibilistic linear systems and their applications to linear regression model, Fuzzy Sets and Systems 27 (1988) 275-289

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V. Vapnik, The Nature of Statistical learning Theory, Springer, 1995
J. Watada, theory of fuzzy multivariate analysis and its applications, PH. D. Dissertation University of Osaka Prefecture, 1983

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Fuzzy regression using regularlization method based on Tanaka's model 원문보기

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Fuzzy regression using regularlization method based on Tanaka's model 원문보기

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