Numerical methods for approximation of fuzzy data

In this work we develop methods to construct polynomials that are consistent with the uncertainty in data {(xi,fi∼)}i=0n. First fuzzy interpolation polynomial (FIP) in form of fuzzy Newton finite difference interpolation problem (FNIP) formula through the extension principle, is introduced then the fuzzy Taylor interpolation problem (FTIP) is resulted and then the uniqueness and convergence theorems are discussed and proved in detail. The FNIP and FTIP maybe interpolates the different fuzzy support points other than above. Thus we approximate them. Fuzzy derivatives for fuzzy function is defined by using the finite differences. Finally the algorithms are illustrated by solving some numerical examples.