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An integrated shrinkage strategy for improving efficiency in fuzzy regression modeling

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Abstract

The fuzzy linear regression (FLR) modeling was first proposed making use of linear programming and then followed by many improvements in a variety of ways. In almost all approaches, researchers put many efforts to change the meters, objective functions, or restrictions to improve the fuzzy goodness of fit (GOF) measures. However, conditions and restrictions in the methods of estimating parameters can reduce efficiency. In this paper, from a different viewpoint, we develop shrinkage strategy, frequently used in classical regression modeling, in the existing FLR to improve GOF measures. In fact, by adding an extra factor to the estimated parameters, without altering the estimation method, the performance of the resulting model is tuned and the GOF measures are improved. However, this method cannot be directly applied since it may give negative spreads for the estimates. Hence, to combat this disadvantage of the shrinkage method, we make refinement and propose an integrated fuzzy shrinkage (IFS) approach. For this approach, an optimal boundary for the shrinkage parameter selection is obtained for which the IFS performs better, comparatively. Further, a fuzzy hypothesis testing procedure is developed to significantly select important coefficients in the FLR model using the p value. Using a simulation study and some illustrative examples, we demonstrate the superiority of the proposed estimation method. In this respect, we show the IFS improves GOF measures dramatically compared to the existing methods.

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Acknowledgements

The authors would like to thank the two anonymous reviewers for their insightful comments which substantially improved the paper.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

    Mojtaba Kashani, Mohammad Reza Rabiei & Mohammad Arashi

Authors
  1. Mojtaba Kashani
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  2. Mohammad Reza Rabiei
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  3. Mohammad Arashi
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Correspondence to Mohammad Reza Rabiei.

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On behalf of all authors of the above titled manuscript, I (as the corresponding author) certify that we have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

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Kashani, M., Rabiei, M.R. & Arashi, M. An integrated shrinkage strategy for improving efficiency in fuzzy regression modeling. Soft Comput 25, 8095–8107 (2021). https://doi.org/10.1007/s00500-021-05690-9

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