Fuzzy Regression Based on Non-Parametric Methods

WSEAS Transactions on Systems and Control

Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 13, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 13, 2018

Fuzzy Regression Based on Non-Parametric Methods

AUTHORS: Seung Hoe Choi, Jin Hee Yoon

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ABSTRACT: In recent years, a number of methods have been proposed to construct fuzzy regression models based the fuzzy distance. Most of the researches that have been proposed have used the parametric methods specifying the form of the relationship between the dependent and independent variables. In this talk, we introduce nonparametric fuzzy regression methods such as Rank transform method, Theil’s method, Kernel method, k-nearest neighborhood method and Median smoothing method and discuss the efficiency of the proposed methods.

KEYWORDS: Rank transform method; Theil’s method; Kernel method; k-nearest neighborhood method; Median smoothing method.

REFERENCES:

[1].Altman, N. S., 1992. An introduction to kernel and nearest-neighbor nonparametric regression, The American Statistician. 46 (3), 175-185.

[2].Bargiela, A., Pedrycz, W., Nakashima, T., 2007. Multiple regression with fuzzy data, Fuzzy Sets and Systems 158, 2169-2188.

[3].Calonico, S., Cattaneo, M. D., Titiunik, R., 2014. Robust Nonparametric Confidence Intervals for RegressionDiscontinuity Designs, Econometrica 82, Issue 6, 2295-2326.

[4].Cheng, C.-B., Lee, E. S., 1999. Nonparametric Fuzzy Regression and Kernel Smoothing Techniques, Computers and Mathematics with Applications 38, 239-251.

[5].Choi, S.H., Jung, H.-Y. Lee, W.-J., Yoon, J.H., 2016. On Theil’s method in fuzzy linear regression models, Commun. Korean Math. Soc. 31(1), 185-198.

[6].Diamond, P., 1988. Fuzzy least squares, Information Sciences 46, 141-157.

[7].Dietz, E. J., 1989. Teaching Regression in a Nonparametric Statistics Course, The American Statistician 43, 35-40.

[8].Dubois, D. and Prade, H., 1979. Fuzzy real algebra and ome results, Fuzzy Sets and Systems 2, 327-348.

[9].Iman, R. L., Conover, W. J., 1979. The Use of the Rank Transform in Regression, Technometrics (c) 21, No 4, 499-509.

[10].Jung H.Y., Lee, W-J., Yoon, J.H., 2014. A unified approach to asymptotic behaviors for the autoregressive model with fuzzy data, Information Sciences 257, 127-137.

[11].Jung H.Y., Yoon, J.H., Choi, S.H., 2015. Fuzzy linear regression using rank transform method, Fuzzy Sets and Systems 274,97-108.

[12].Kim, H.K., Yoon, J.H., Li, Y., 2008. Asymptotic properties of least squares estimation with fuzzy observations, Information Sciences 178, 439-451.

[13].Kao, C., Lin, P., 2005. Entropy for fuzzy regression analysis, Int. Journal of Sys. Sci., 36, 869-876.

[14].Kim, K.J., Chen, H.-R., 1997. A Comparison of Fuzzy and Nonparametric Linear Regression, Computers Ops.Res., 24, No. 6, 505-519.

[15].Lee, W-J., Yoon, J.H., Jung, H-Y., Choi, S.H., 2015. The statistical inferences of fuzzy regression based on bootstrap techniques, Soft Comput. 19, 883-890.

[16].Lee, W-J., Jung, H-Y., Yoon, J.H., Choi, S.H., 2017. A Novel Forecasting Method Based on F-Transform and Fuzzy Time Series, Int. J. Fuzzy Syst. 19(6), 1793-1802.

[17].Nevitt, J., Tam, H. P., 1998. A Comparison of Rosbust and Nonparametirc Estimators Under the Simple Linear Regression Model Multiple Linear Regression Viewpoints, 25, 54-69.

[18].Tanaka, H., Uejima, S., Asai, K., 1982. Linear regression analysis with fuzzy model, IEEE Trans. Systems, Man Cybernet 12, 903-907.

[19].Razzaghnia, T., Danesh, S., 2015. Nonparametric Regression with Trapezoidal Fuzzy Data, International Journal on Recent and Innovation Trends in Computing and Communication 3, 3 Issue 6, 3826-3831.

[20].Theil, H., 1950. A rank invariant of linear and polynomial regression analysis, Pro. Kon. Ned. Akad. Wetensch. A, 53, 386-392.

[21].Wang, N., Zhang, W.-X., Mei, C.-L., 2007. Fuzzy nonparametric regression based on local linear smoothing technique, Information Sciences 177, 3882-3900.

[22].Wu, H.-C., 2008. Fuzzy linear regression model based on fuzzy scalar product, Soft Computing 12, 469-477.

[23].Yoon, J.H., Choi, S.H., 2013. Fuzzy Least Squares Estimation with New Fuzzy Operations, Synergies of Soft Computing and Statistics, AISC 190, 193-202.

[24].Yoon, J.H., Choi, S.H., Grzegorzewski, P., 2016. On Asymptotic Properties of the Multiple Fuzzy Least Squares Estimator, Soft Methods for Data Science, 525-532.

[25].Zadeh, L.A., 1965. Fuzzy sets, Information and control 8, 338-353.

[26].Zadeh, L.A., 1975. The Concept of a Linguistic Variable and its Application to Approximate Reasoning-I, Information science 8, 199-246.

WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 13, 2018, Art. #3, pp. 20-25

Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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