In this manuscript, three contributions are proposed. First contribution is proposing a good evaluation between the fuzzy and neutrosophic approaches using a novel fuzzy-neutrosophic transfer. Second contribution is introducing a general framework for solving the neutrosphic linear programming problems using the advantages of the method of Abdel-Basset et al. and the advantages of Singh et al.'s method. Third contribution is proposing a new neutrosophic exterior point simplex algorithm NEPSA and its fuzzy version FEPSA. NEPSA has two paths to get optimal solutions. One path consists of basic not feasible solutions but the other path is feasible. Finally, the numerical examples and results analysis show that NEPSA more than accurate FEPSA.