In this paper, a new set of spline functions called \Flat End Fuzzy Spline" is de ned to interpolate given fuzzy data. Some important theorems on these splines together with their existence and unique-ness properties are discussed. Then numerical examples are presented to illustrate the di erences between of using our spline and other interpolations that have been studied before.

In this paper,  rstly, we review approximation of fuzzy functions by fuzzy bicubic splines interpo-lation and present a new approach based on the two-dimensional fuzzy splines interpolation and iterative method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equa-tion (2DLFFIE). Also, we prove convergence analysis and numerical stability analysis for the proposed numerical algorithm. Finally, by an example, we show the e ciency of the proposed method.

Purpose: In this paper, we will consider the interpolation of fuzzy data by using the fuzzy-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 of interpolation 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 will apply 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 functions was 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 extra term to this spline to compute the piecewise quartic polynomials and hence the fuzzy-valued piecewise quartic polynomials.