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MADM approach to analyse the performance of fuzzy regression models

Abstract

It is worth to note that estimated parameters of any fuzzy regression model as well as its goodness-of-fit value depend on the objective function being optimized. Thus, it is not easy to compare the solutions of different models that optimize different objective functions. On the other hand, dataset has a significant influence on the performance of any model estimation procedure making the comparison more challengeable. In this paper, we propose a method in order to compare and/or rank a set of fuzzy regression models based on their goodness-of-fit performance analysis when applied to modeling a dataset. With regard to that, the problem of finding the most preferred/desirable model is considered as a multi-attribute decision making (MADM) problem in which the set of candidate models are alternatives and the goodness-of-fit criteria are attributes. Attribute values are calculated based on well-known goodness-of-fit formula while their weights, which are considered as the most important points in MADM problems, are calculated by the entropy measure. Therefore, the entries of the decision matrix are considered as the fitness values of the data points by the models (or alternatives). The entropy values are then transformed to the weight values of the data points illustrating the importance of each data point in the estimation methods of models. Ultimately, the TOPSIS method is employed to provide an algorithm to rank the models. The proposed method not only gives us the rank of the models, but also provides us an index showing how much each ranked model fits the data set.

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Acknowledgements

The Authors would like to thank the reviewers for the thoughtful comments and the constructive suggestions which helped to improve the quality of this manuscript. They also appreciate the Editor’s warm work earnestly, which helped to make the manuscript suitable for possible publication in the eminent journal.

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Correspondence to Jalal Chachi.

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Kazemifard, A., Chachi, J. MADM approach to analyse the performance of fuzzy regression models. J Ambient Intell Human Comput (2021). https://doi.org/10.1007/s12652-021-03394-4

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Keywords

  • Fuzzy regression
  • Multi-attribute decision making (MADM)
  • Entropy
  • Performance analysis
  • TOPSIS