<p>The mean–variance–skewness portfolio selection model optimizes investment portfolios by considering the mean, variance, and skewness of different assets, aiming to construct a portfolio that maximizes expected return while minimizing risk and maximizing skewness. This model endeavors to achieve a harmonious equilibrium between risk and return by taking into account not only the average return and risk but also the asymmetrical characteristics of returns. Through the inclusion of skewness in the portfolio selection process, investors can gain a comprehensive perspective on the likelihood of experiencing exceptional positive or negative returns. In order to compute skewness of total uncertain returns, this paper presents the concept of co-skewness for uncertain variables. Also, a formula for calculating of co-skewness is obtained via inverse uncertainty distributions and applied to Monte-Carlo simulation. As an application of skewness, mean–variance–skewness portfolio optimizations are provided.</p>