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

Authors

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

2 Department of Statistics, Payame Noor University, Iran

Abstract

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.

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References

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Journal of Advanced Mathematical Modeling
Volume 9, Issue 2
September 2019
Pages 1-32

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History

  • Receive Date: 05 November 2017
  • Revise Date: 06 July 2019
  • Accept Date: 02 August 2019

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