Abdolmajid Abdolbaghi Ataabadi - management, Faculty of Industrial Engineering and Management , shahrood university of technology
Alireza Nazemi - Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
Masoumeh Saki - Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran

In this paper, we use fuzzy numbers and possibility theory to model possibility. The purpose of this work is to determine the optimal investment model based on the neural network method for fuzzy LR, trapezoidal and triangular numbers in an optimal portfolio. It is listed on the Tehran Stock Exchange to maximize "returns" and reduce "risk" to find the optimal portfolio. Therefore, to achieve this goal, the problem of multi-objective nonlinear programming is addressed. Also, by substituting the mean-variance model and the standard mean deviation instead of the Markowitz mean-variance model, the selection of the optimal portfolio in the possible space is examined. Finally, after calculating the model of the possibility of fuzzy numbers, we reach the optimal stock portfolio, which can be used to set the stock portfolio that has the highest returns and the lowest risk.

Mean-variance model, Optimal portfolio, Possibility space, Objective functions