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A Fuzzy-Statistical Tolerance Interval from Residuals of Crisp Linear Regression Models

Author

Listed:
  • Maryam Al-Kandari

    (Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Khaldiyah City, Kuwait)

  • Kingsley Adjenughwure

    (Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece)

  • Kyriakos Papadopoulos

    (Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Khaldiyah City, Kuwait)

Abstract

Linear regression is a simple but powerful tool for prediction. However, it still suffers from some deficiencies, which are related to the assumptions made when using a model like normality of residuals, uncorrelated errors, where the mean of residuals should be zero. Sometimes these assumptions are violated or partially violated, thereby leading to uncertainties or unreliability in the predictions. This paper introduces a new method to account for uncertainty in the residuals of a linear regression model. First, the error in the estimation of the dependent variable is calculated and transformed to a fuzzy number, and this fuzzy error is then added to the original crisp prediction, thereby resulting in a fuzzy prediction. The results are compared to a fuzzy linear regression with crisp input and fuzzy output, in terms of their ability to represent uncertainty in prediction.

Suggested Citation

  • Maryam Al-Kandari & Kingsley Adjenughwure & Kyriakos Papadopoulos, 2020. "A Fuzzy-Statistical Tolerance Interval from Residuals of Crisp Linear Regression Models," Mathematics, MDPI, vol. 8(9), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1422-:d:403632
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    References listed on IDEAS

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    1. Xilong Liu & Yizeng Chen, 2013. "A Systematic Approach to Optimizing Value for Fuzzy Linear Regression with Symmetric Triangular Fuzzy Numbers," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, December.
    2. Kim, Kwang Jae & Moskowitz, Herbert & Koksalan, Murat, 1996. "Fuzzy versus statistical linear regression," European Journal of Operational Research, Elsevier, vol. 92(2), pages 417-434, July.
    3. Young, Derek S., 2010. "tolerance: An R Package for Estimating Tolerance Intervals," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i05).
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