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A novel computational approach to approximate fuzzy interpolation polynomials.

Ahmad Jafarian1, Raheleh Jafari2, Maysaa Mohamed Al Qurashi3

  • 1Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.

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|September 15, 2016
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Summary

This study introduces a fuzzy neural network for fuzzy interpolation polynomial approximation. Numerical experiments confirm this novel method is reliable and efficient for interpolating fuzzy data.

Keywords:
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Area of Science:

  • Fuzzy mathematics
  • Artificial intelligence
  • Numerical analysis

Background:

  • Fuzzy interpolation is crucial for approximating functions with imprecise data.
  • Traditional methods may struggle with the complexity of fuzzy data.
  • Developing robust interpolation techniques for fuzzy sets is an ongoing challenge.

Purpose of the Study:

  • To construct a fuzzy neural network (FNN) capable of fuzzy interpolation.
  • To estimate unknown coefficients of a fuzzy interpolation polynomial using neural networks.
  • To demonstrate the reliability and efficiency of the proposed FNN-based interpolation method.

Main Methods:

  • A novel fuzzy neural network structure is developed.
  • A gradient descent algorithm is employed to train the FNN.
  • The FNN learns to estimate coefficients for a fuzzy interpolation polynomial of the form [Formula: see text].

Main Results:

  • The proposed FNN successfully generates a fuzzy interpolation polynomial.
  • The gradient descent training effectively estimates the unknown polynomial coefficients.
  • Numerical experiments validate the accuracy and performance of the interpolation technique.

Conclusions:

  • The developed fuzzy neural network provides an effective approach for fuzzy interpolation.
  • The gradient descent training ensures reliable estimation of fuzzy polynomial coefficients.
  • The methodology is proven to be both reliable and efficient for interpolating fuzzy data.