Investment in real economic activities is generally uncertain and stochastic, and investors' choice of risky assets is of multi-stage in most cases. Based on this reality, multiple frictions in a fuzzy environment are considered and a base constraint is proposed on assets using transaction restrictions to develop a likelihood mean-lower half-variance-entropy multi-stage portfolio optimization model (V-S-M), which is a multi-stage mixed integer programming problem. A genetic differential co-evolutionary algorithm (GAHDE) for solving the model is presented to analyse the portfolio strategy under different risk attitudes, and the numerical results are compared with the likelihood mean-lower half variance model (V-M) and the likelihood mean-entropy model (S-M), as well as with standard genetic algorithms (GA) and differential evolution algorithms (DE). The results validated the superiority and effectiveness of the model and algorithm designed in this paper.