Approximation of a Fuzzy Function by Using Radial Basis Functions Interpolation

Subject Areas : International Journal of Mathematical Modelling & Computations

Reza Firouzdor ¹ , Majid Amirfakhrian ²

1 - university
2 - IAUCTB

Received: 2016-11-03 Accepted : 2018-08-26 Published : 2017-11-01

Keywords: Radial Basis Function interpolation, fuzzy function, fuzzy-valued function, an approximation of a fuzzy function,

Abstract :

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $\tilde{f}:\R\rightarrow \mathcal{F}(\R)$, on a discrete point set $X=\{x_1,x_2,\ldots,x_n\}$, by a fuzzy-valued function $\tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system will be obtained which by defining coefficient vector, target function will be approximated. Finally for showing the efficiency of the method we give some numerical examples.