Abstarct: In this research, we apply the feasibility modeling by applying a variety of fuzzy numbers and using the possibility theory to determine the optimal investment model baxsed on neural network methodology for fuzzy $ L-R $, trapezoidal and triangular numbers in optimal portfolio formation. Securities. The overall goal is to maximize "return" and reduce "risk" to find the optimal portfolio. So, to achieve this goal, solve the multi-objective nonlinear programming problem using the Zimmerman method by minimizing the objective functions. Furthermore, by replacing the mean-variance and standard deviation models by the Markovits mean-variance model, consider the optimal portfolio selection in the Possibilistic space.