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Fuzzy Regression Analysis Based on Fuzzy Neural Networks Using Trapezoidal Data

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Abstract

Fuzzy regression is a generalized regression model to represent the relationship between dependent and independent variables in a fuzzy environment. The fuzzy linear regression analysis seeks for regression models fitting well all the data based on a specific criterion. In this paper, an adaptive neuro-fuzzy inference system (ANFIS) is employed for the analysis and prediction of a nonparametric fuzzy regression function with non-fuzzy inputs and symmetric trapezoidal fuzzy outputs. To this end, two new hybrid algorithms are proposed in which the fuzzy least squares and linear programming have been used to optimize the secondary weights. The algorithms are applied to a multi-layered validation method to confirm the models’ reliability. In addition, three methods of nonparametric fuzzy regression with crisp inputs and asymmetric trapezoidal fuzzy outputs, are compared. Three nonparametric techniques in statistics, namely local linear smoothing (L-L-S), K-nearest neighbor smoothing (K-NN) and kernel smoothing (K-S) with trapezoidal fuzzy data have been analyzed to obtain the best smoothing parameters. The performance of the models is illustrated through numerical examples and simulations. More specifically, the accuracy of the algorithms is confirmed by exhaustive simulations.

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Abbreviations

\({MF}_{i}\) :

Membership function

\(\stackrel{\sim }{{Y}_{i}}\) :

A trapezoidal fizzy number

\({o}_{k.i}\) :

Placed as layers

\(d^{2} \left( {\tilde{Y}_{i} \cdot \widehat{{Y_{i} }}} \right)\) :

Diamond distance measures

\(\left( \widehat{{\widetilde{{Y_{i} }}}} \right)\) :

A predicted of a trapezoidal fuzzy number

\({\omega }_{j}\left(x\right)\) :

Weight sequence at \(x\)

\(CV\) :

Cross-validation

k(.):

Kernel smoothing

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Authors and Affiliations

  1. Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    R. Naderkhani & M. H. Behzad

  2. Department of Statistics, North Tehran Branch, Islamic Azad University, Tehran, Iran

    T. Razzaghnia

  3. School of Mathematics, Iran University of Science and Technology, Narmak, 16846, Tehran, Iran

    R. Farnoosh

Authors
  1. R. Naderkhani
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  2. M. H. Behzad
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  3. T. Razzaghnia
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  4. R. Farnoosh
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Correspondence to T. Razzaghnia.

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Naderkhani, R., Behzad, M.H., Razzaghnia, T. et al. Fuzzy Regression Analysis Based on Fuzzy Neural Networks Using Trapezoidal Data. Int. J. Fuzzy Syst. 23, 1267–1280 (2021). https://doi.org/10.1007/s40815-020-01033-2

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  • DOI: https://doi.org/10.1007/s40815-020-01033-2

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