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.
Fuzzy arithmetic Generalized variance inflation factor Goodness of fit Fuzzy ridge regression
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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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Conflict of interest
The authors declare that they have no conflict of interest.
This article does no contain any studies with human participants or animals performed by any of the authors.
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