Portfolio Selection Models Considering Fuzzy Preference Relations of Decision Makers

During the portfolio selection process, investors often have individual behavioral preferences that may be fuzzy, uncertain, and incomplete. For the first time, this article combines fuzzy preference relations (FPRs) with portfolio theory to study the portfolio selection problem faced by investors. First, we improve the relations between judgment elements and priority vectors in FPRs and develop a new definition of additively consistent FPRs under priority vectors. On the basis of this and Markowitz portfolio models, we then propose two portfolio models considering FPRs with unknown preference information and three types of portfolio models considering FPR with partially known preference information. We conduct a comparative analysis of these models and derive a flowchart of investment selection under different conditions. Finally, we use an empirical example to compare the results of all models and analyze their sensitivity to various parameters. The results demonstrate that increasing the distance threshold between judgment elements has a positive effect on the objective function of portfolio models considering FPRs, although this effect gradually becomes saturated. Additionally, the models proposed in this article exhibit high robustness to the consistency index of FPRs.