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

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AKBARI MOHAMMAD GHASEM; Hesamian Gholamreza

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2019 | Volume:9 | Issue:2 Page(s): 1-32

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Information Journal Paper

Title

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

Author(s)

AKBARI MOHAMMAD GHASEM | Hesamian Gholamreza | Issue Writer Certificate

Keywords

Fuzzy observationQ1

Fuzzy hypothesisQ1

Confidence intervalQ1

BootstrapQ2

Distance measure between two fuzzy numbersQ1

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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APA: Copy

AKBARI, MOHAMMAD GHASEM, & Hesamian, Gholamreza. (2019). 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. ADVANCES IN MATHEMATICAL MODELING, 9(2 ), 1-32. SID. https://sid.ir/paper/243875/en

Vancouver: Copy

AKBARI MOHAMMAD GHASEM, Hesamian Gholamreza. 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. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2019;9(2 ):1-32. Available from: https://sid.ir/paper/243875/en

IEEE: Copy

MOHAMMAD GHASEM AKBARI, and Gholamreza Hesamian, “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,” ADVANCES IN MATHEMATICAL MODELING, vol. 9, no. 2 , pp. 1–32, 2019, [Online]. Available: https://sid.ir/paper/243875/en

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