Optimal Portfolio Selection is one of the most important issues in the field of financial research. In the present study, we try to compare four various different models, which optimize three-objective portfolios using “Postmodern Portfolio Optimization Methods”, and then to solve them. These modeling approaches take into account both multidimensional nature of the portfolio selection problem and requirements imposed by investors. Concretely different models optimize the expected return, the down side risk, skewness and kurtosis given portfolio, taking into account budget, bounds and cardinality constrains. The quantification of uncertainty of the future returns on a given portfolio is approximated by means of LR-fuzzy numbers, while the moments of its returns are evaluated using possibility theory. In order to analyze the efficient portfolio, which optimize three criteria simultaneously, we build a new NSGAII algorithm, and then find the best portfolio with most Sortio ratio from the gained Pareto frontier. Thus, in this paper we choose 153 different shares from different industries and find their daily return for ten years from April of 2006 till March of 2017 and then we calculate their monthly return, downside risk, skewness, kurtosis and all of their fuzzy moments. After designing the four models and specific algorithm, we solve all of the four models for ten times and after collection of a table of the answers, compare all of them with Treyner ratio. At last, we find that using fuzzy and possibistic theory make higher return and better utilized portfolios.