10.1186/2251-7456-6-40

Interpolation of fuzzy data by using quartic piecewise polynomials induced from E(3) cubic splines

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  • Hossein Behforooz*1,
  • Reza Ezzati2,
  • Saeid Abbasbandy3,
  1. Department of Mathematics, Utica College, Utica, NY, 13502, US
  2. Department of Mathematics, Islamic Azad University, Karaj, 31485, IR
  3. Department of Mathematics, Imam Khomeini International University, Ghazvin, 34194, IR
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Published in Issue 2012-10-03

How to Cite

Behforooz, H., Ezzati, R., & Abbasbandy, S. (2012). Interpolation of fuzzy data by using quartic piecewise polynomials induced from E(3) cubic splines. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-40
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Abstract

Abstract Purpose In this paper, we will consider the interpolation of fuzzy data by using thefuzzy-valued piecewise quartic polynomials Qy0,y1,…,yn(x) induced from E (3) cubic spline functions. Method It has been many years since researchers have attended to the problem ofinterpolation of fuzzy data. Here, for Lagrange interpolation of fuzzy data,we will use the piecewise quartic polynomial induced from E (3)cubic spline functions to interpolate the fuzzy data. To do this, we willapply the extension principle to construct the membership function of Qy0,y1,…,yn(x) . Results By using piecewise quartic polynomials, a new set of fuzzy spline functionswas defined to interpolate given fuzzy data. Conclusions In our previous study, we used E (3) cubic spline to construct E (3) fuzzy cubic spline. In this article, we added one extraterm to this spline to compute the piecewise quartic polynomials and hencethe fuzzy-valued piecewise quartic polynomials.

Keywords

  • E(3) cubic spline,
  • Quartic piecewise polynomials,
  • Fuzzy interpolation,
  • Extension principle,
  • 94D05,
  • 26E50
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References

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