Statistical inference of fuzzy weighted regression based on bootstrap approach

Document Type : Original Article

Authors

Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

In this article, the hypothesis test and confidence interval for the fuzzy coefficients in the fuzzy weighted regression model with precise inputs and fuzzy outputs are discussed. By applying the weighted estimation method in estimating the coefficients and using the conventional fuzzy hypotheses in the fuzzy environment,, We are trying to determine the distribution of the available estimators, based on the bootstrap method so that we can decide to accept or reject the existing hypotheses. Therefore, at first, the required test statistics are calculated based on the bootstrap method. Then, by comparing the probability value and the given significance level, as in the classical method, the null hypothesis is accepted or rejected. Also, from another point of view, hypothesis testing based on bootstrap confidence intervals is also discussed. At the end, by analyzing a practical example with real data in housing, the approach investigated in hypothesis testing and confidence interval for the coefficients of the fuzzy regression model has been analyzed.

Keywords

Main Subjects


[1] اکبری, م. ق. و حسامیان, غ.  (1398).  بهبود یک روش آزمون فرضیه و فاصله اطمینان در رگرسیون خطی تک متغیره فازی،
مجله مدل‌سازی پیشرفته ریاضی, دوره  9، شماره 2, ص ص  1-32.
 
[2] چاچی، ج.، کاظمی‌فرد، ا. و فهیمی، ح . (1400). رهیافت تصمیم‌گیری‌های چند معیاره در ارزیابی نیکویی برازش مدل‌های آماری،
سیستم‌های فازی و کاربردها،  دوره 4،  شماره 1، ص ص 247-267.
 
[3] چاچی، ج. و چاجی، ع.  (1397). رویکردهای وزنی در برازش مدل‌های رگرسیون فازی، سیستم‌های فازی و کاربردها،
 دوره 1،  شماره 2، ص ص 105-117.
 
[4] رضایی، ک. و رضایی، ح . (1397). بررسی معیارهای فاصله و شباهت برای مجموعه‌های فازی و برخی از توسعه‌های آنها،
سیستم‌های فازی و کاربردها، دوره 1، شماره 2، پاییز و زمستان 1397، ص ص 45-104.
 
[5] Arefi, A. (2020). Quantile fuzzy regression based on fuzzy outputs and fuzzy parameters, Soft Computing, 24, 311-320.
 
[6] Celmins, A. (1987). Least squares model fitting to fuzzy vector data, Fuzzy Sets and Systems, 22, 245–269.
 
[7] Chachi, J. (2019). A Weighted Least Squares Fuzzy Regression for Crisp Input Fuzzy Output Data, IEEE Transactions on Fuzzy Systems, 27(4), 739–748.
 
[8] Chachi, J. and Chaji, A. (2021). An OWA-Based Approach to Quantile Fuzzy Regression. Computers and Industrial Engineering, 159, 107498.
 
[9] Chachi, J., Taheri, S.M. and D’Urso, P. (2022). Fuzzy Regression Analysis Based on M-estimates, Expert Systems with Applications, 187, 115891.
 
[10] Chukhrova, N. and Johannssen, A. (2019). Fuzzy Regression Analysis: Systematic Review and Bibliography, Applied Soft Computing, 84, 105708.
 
[11] Diamond, P. (1988). Fuzzy least squares, Information Sciences, 46, 141-157.
 
[12] D’Urso, P. and Chachi, J. (2022). Owa fuzzy regression, International Journal of Approximate Reasoning, 142, 430-450.
 
[13] D’Urso, P. and Massari, R. (2013). Weighted least squares and least median squares estimation for the fuzzy linear regression analysis, Metron, 71, 279-306.
 
[14] D’Urso, P., Massari, R., Santoro, A. (2011). Robust fuzzy regression analysis, Information Sciences, 181, 4154-4174.
 
[15] Efron, B. and Raoul, L. (1992). Introduction to Bootstrap. Wiley & Sons, New York.
 
[16] Ferraro, M. B. (2017). On the generalization performance of a regression model with imprecise elements. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 25, 723-740.
 
[17] Hesamian, G. and Akbari, M.G. (2017). Semi-parametric partially logistic fuzzy regression model with exact inputs and intuitionistic fuzzy outputs, Applied Soft computing, 58, 517-526.
 
[18] Hesamian, G. and Akbari, M.G. (2020). A Robust Varying Coefficient Approach to Fuzzy Multiple Regression Model, Journal of Computational and Applied Mathematics, 371, 112704.
 
[19] Hesamian, G. and Akbari, M.G. (2020). Fuzzy spline univariate regression with exact predictors and fuzzy responses, Journal of Computational and Applied Mathematics, 375, 112803.
 
[20] Hesamian, G. and Akbari, M.G. (2021). A Robust Multiple Regression Model Based on Fuzzy Random Variables, Journal of Computational and Applied Mathematics, 388, 113270.
 
[21] Hesamian, G. and Akbari, M.G. (2021). A Fuzzy Additive Regression Model with Exact Predictors and Fuzzy Responses, Applied Soft Computing, 95, 106507.
 
[22] Hesamian, G., Akbari, M.G. and Shams, M. (2021). Parameter Estimation in Fuzzy Partial Univariate Linear Regression Model with Non-Fuzzy Inputs and Triangular Fuzzy Outputs, Iranian Journal of Fuzzy Systems, 18, 51–64.
 
[23] Kazemifard, A. and Chachi, J. (2021). MADM Approach to Analyse the Performance of fuzzy regression models. Journal of Ambient Intelligence and Humanized Computing, 13, 4019–4031.
 
[24] Khammar, A.H., Arefi, M. and Akbari, M.G. (2020). A Robust Least-Squares Fuzzy Regression Model Based on Kernel Function, Iranian Journal of Fuzzy Systems, 17, 105–119.
 
[25] Khammar, A.H., Arefi, M. and Akbari, M.G. (2021). A General Approach to Fuzzy Regression Models Based on Different Loss Functions, Soft Computing, 25, 835–849.
 
[26] Khammar, A.H., Arefi, M. and Akbari, M.G. (2021). Quantile fuzzy varying coefficient regression based on kernel function, Applied Soft Computing, 107, 107313.
 
[27] Leski, J.M. and Kotas, M. (2015). On robust fuzzy c-regression models, Fuzzy Sets and Systems, 279, 112-129.
 
[28] Tanaka, H., Hayashi, I. and Watada, J. (1989). Possibilistic linear regression analysis for fuzzy data, European J. Operational Research, 40, 389-396.
 
[29] Tanaka, H., Uegima, S. and Asai, K. (1982). Linear regression analysis with fuzzy model, IEEE Trans. Syst. Man Cybernet., 12, 903-907.
 
[30] Zhou, J., Zhang, H., Gu1, Y. and Pantelous, A.A. (2018). Affordable levels of house prices using fuzzy linear regression analysis: the case of Shanghai, Soft Computing, 22, 5407-5418.
 
[31] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8, 338-353.
 
[32] Zimmermann, H.J. (2001). Fuzzy Set Theory and Its Applications, 4th ed., Kluwer Nihoff, Boston.