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Soft Computing

, Volume 23, Issue 23, pp 12189–12198 | Cite as

Fuzzy ridge regression with fuzzy input and output

  • Mohammad Reza RabieiEmail author
  • Mohammad Arashi
  • Masoumeh Farrokhi
Foundations
  • 48 Downloads

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.

Keywords

Fuzzy arithmetic Generalized variance inflation factor Goodness of fit Fuzzy ridge regression 

Notes

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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does no contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Mohammad Reza Rabiei
    • 1
    Email author
  • Mohammad Arashi
    • 1
  • Masoumeh Farrokhi
    • 1
  1. 1.Department of Statistics, Faculty of Mathematical SciencesShahrood University of TechnologyShahroodIran

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