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Journal of Mathematical Chemistry

, Volume 57, Issue 5, pp 1252–1267 | Cite as

Approximation of fuzzy functions by fuzzy interpolating bicubic splines: 2018 CMMSE conference

  • P. GonzálezEmail author
  • H. Idais
  • M. Pasadas
  • M. Yasin
Original Paper
  • 132 Downloads

Abstract

One of the most interesting and important techniques in applied mathematics is interpolation and approximation. It can be also shown that basic theory of fuzzy sets and operations with fuzzy numbers can be used, and result very convenient, for solving many analytical chemistry problems: as depth profile comparison or calibration with errors in signals and/or concentrations, for spectra interpretation, or even for automatic qualitative analysis or expert systems with X-ray spectroscopy. In this special context, we introduce in this paper a new fuzzy interpolation method of fuzzy data or functions, specially indicated in all these chemical applications. We will use bicubic splines (cubic splines of two variables) of class \(\mathcal {C}^2\) as linear combinations of a basis constructed by a tensor product of univariate B-splines in each of these variables. First we establish a bicubic interpolation spline method of a given fuzzy data set or a given fuzzy bivariate function. We proof the existence of a unique solution of this problem and we show a convergence result. Finally, we test the effectiveness of this method by some numerical and graphical examples.

Keywords

Interpolation and approximation Fuzzy data Bicubic splines Analytical chemistry Calibration Spectroscopy 

Notes

Acknowledgements

We would like to thanks the financial and logistic aid granted by the Department of Applied Mathematics of the University of Granada for the accomplishment of this research work and the possibility to present it at the 2018 CMMSE International Conference.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Dpto. de Matemática AplicadaUniv. de GranadaGranadaSpain

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