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Fuzzy ridge regression with fuzzy input and output

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Abstract

In regression modeling, existence of multicollinearity may result in linear combination of the parameters, leading to produce estimates with wrong signs. In this paper, a fuzzy ridge regression model with fuzzy input–output data and crisp coefficients is studied. We introduce a generalized variance inflation factor, as a method to identify existence of multicollinearity for fuzzy data. Hence, we propose a new objective function to combat multicollinearity in fuzzy regression modeling. To evaluate the fuzzy ridge regression estimator, we use the mean squared prediction error and a fuzzy distance measure. A Monte Carlo simulation study is conducted to assess the performance of the proposed ridge technique in the presence of multicollinear data. The fuzzy coefficient determination of the fuzzy ridge regression model is higher compared to the fuzzy regression model, when there exists sever multicollinearity. To further ascertain the veracity of the proposed ridge technique, two different data sets are analyzed. Numerical studies demonstrated the fuzzy ridge regression model has lesser mean squared prediction error and fuzzy distance compared to the fuzzy regression model.

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Acknowledgements

The authors would like to thank two anonymous reviewers for their constructive comments which led to put many details in the paper and significantly improved the presentation.

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Authors and Affiliations

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

    Mohammad Reza Rabiei, Mohammad Arashi & Masoumeh Farrokhi

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  1. Mohammad Reza Rabiei
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  2. Mohammad Arashi
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  3. Masoumeh Farrokhi
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Correspondence to Mohammad Reza Rabiei.

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Rabiei, M.R., Arashi, M. & Farrokhi, M. Fuzzy ridge regression with fuzzy input and output. Soft Comput 23, 12189–12198 (2019). https://doi.org/10.1007/s00500-019-04164-3

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