An Improved Method Estimating and Performing Confidence Interval and Hypothesis Test in a Fuzzy Simple Linear Regression Model With non-fuzzy Inputs And Fuzzy outputs

Document Type : Original Paper


1 Department of Statistics, University of Birjand, Birjand, Iran

2 Department of Statistics, Payame Noor University, Iran


In this paper, an existing method to estimate coefficients of a fuzzy regression model with non-fuzzy inputs and fuzzy out-puts as well as its method to perform a fuzzy hypothesis test and a fuzzy confidence interval are recalled. Then, the disadvantages and shortcoming of this method are examined and criticized by analyzing several numerical examples. By introducing an appropriate alternative approach to estimating coefficients and applying conventional fuzzy hypotheses in a fuzzy environment, we try to improve the method in the structure and decision making to accept or reject fuzzy hypotheses. For this purpose, employing a common distance measure and Bootstrap technique, the required test statistics are defined as non-fuzzy criteria. Then, by comparing the p-value obtained from the test statistics and a given significance, unlike the existing one, one can easily decide to accept or reject the null hypothesis. Also, using some applied examples, the possible advantageous of the proposed approach in hypothesis testing and confidence interval for fuzzy coefficients are compared and discussed.


Main Subjects

[1] Diamond, P. and Korner, R. (1997). Extended fuzzy linear models and least squares estimates. Computers and Mathematics with Applications, 33, 15-32.
[2] Mohammadi, J. and Taheri, S. M. (2004). Pedomodels ffitting with fuzzy least squares regression. Iranian Journal of Fuzzy Systems, 1, 45-62.
[3] Lee, W. J., Jung, H. Y., Yoon, O. J. H. and Choi, S. H. (2014). The statistical inferences of fuzzy regression based on bootstrap techniques. Soft Computing, 19, 883-890.
[4] Kao, C. and Chyu, C. L. (2003). Least-squares estimates in fuzzy regression analysis. European Journal of Operational Research, 148, 426-435.
[5] Choi, S. H. and Buckley, J. J. (2008). Fuzzy regression using least absolute deviation estimators. Soft Computing, 12, 257-263.
[6] Ferraro, M. B. and Coppi, R., Gonazlez-Rodriguez, G. and Colubi, A. (2010). A linear regression model for imprecise response. International Journal of Approximate Reasoning, 51, 759-770.
[7] Chachi, J. and Taheri, S. M. (2013). A least-absolutes regression Model for imprecise response based on the generalized hausdorff-metric. Journal of Uncertain Systems, 7, 265-276.
[8] Lee, W. J., Jung, H. Y., Yoon, O. J. H. and Choi, S. H. (2014). The statistical inferences of fuzzy regression based on bootstrap techniques. Soft Computing, 19, 883-890.
[9] Zadeh, L. A. (1956). Fuzzy sets. Information and Control, 8, 338-353.
[10] Stefanini, L. (2010). A generalization of hukuhara difference for interval and fuzzy arithmetic. Fuzzy Sets and Systems, 161, 1564-1576.
[11] Heilpern, S. (1997).  Representation and application of fuzzy numbers, Fuzzy sets and Systems, 91, 259-268.
[12] Hardy, G. H.Littlewood, J. E. and  Pólya, G. (1952). Inequalities. Cambridge Mathematical Library (second Ed.). Cambridge: Cambridge University Press.
 [13] Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. Society of Industrial and Applied Mathematics CBMS-NSF Monographs, Philadelphia. ISBN 0898711797.