gH-differentiable of the 2th-order functions interpolating

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear combination for 5th degree polynomials linear space and same approach develops to introduce 5th degree fuzzy piecewise Hermite interpolation polynomials. At first, construction method along with an example has presented for 5 th degree fuzzy Hermite interpolation. Because of the introduced method applies for interpolation of first order Generalized Hukuhara differentiable functions so during an example cubic fuzzy Hermite interpolation polynomial compares with fuzzy Hermite polynomial and we explain the superiority of the presented piecewise method next in the end we provide 5th degree fuzzy piecewise Hermite interpolation polynomial. Using such interpolant shows that the smoothness condition improves for interpolation polynomial core when successive degree of fuzzy piecewise Hermite interpolation polynomial comes up from three to five.