Weighting approaches in fitting fuzzy regression models

Document Type : Original Article

20.1001.1.27174409.1397.1.2.5.8/DOR

Abstract

In this paper, we replace the objective functions of fuzzy regressions with the fitting criteria of least squares error and minimum absolute value of deviations (errors) with objective functions based on the weighted sum of functions of errors (deviations or residuals) or ordered errors. According to the method of selecting the optimal weights and the type of function applied to the errors, the solid and unstable approaches common in fuzzy regression models are generalized based on new relationships based on such good fit criteria. We will also make a brief reference here to the calculations related to the optimization problems of such models. Such approaches have a great impact on reducing the destructive effects of Pert observations in estimating the optimal model and are a good alternative to fuzzy regression models with the ability to detect Pert observations. On the other hand, these methods are generalizations of fuzzy regression models of least squares and least absolute values ​​of deviations and can be used to model any combination of input-accurate / fuzzy and output-accurate / fuzzy observations.

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References

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History

  • Receive Date: 19 January 2019
  • Accept Date: 16 April 2019

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