Multi-criteria Group Decision-Making Portfolio Optimization Based on Variable Subscript Hesitant Fuzzy Linguistic Term Sets

This paper applies the cumulative prospect theory to improve the traditional integer subscript hesitant fuzzy linguistic term set (IS-HFLTS). The proposed variable subscript hesitant fuzzy language set (VS-HFLTS) takes into account the subjectivity and differences of investors' behavior when investing in the securities market, and extends the application of behavioral finance to multi-criteria group decision-making portfolio. To evaluate the financial products, the VS-HFLTS multi-criteria group decision-making portfolio evaluation system is constructed in the research. The hesitant fuzzy linguistic value function and the purchase appetite weight function are proposed to convert the natural linguistic evaluation into a quantitative score for the judgment of future portfolio return in the securities market. Furthermore, a variable subscript hesitant fuzzy linguistic portfolio model is put forward for the risk-averse, risk-neutral, and risk-seeking investment decision-makers. The optimal portfolio strategy is obtained by solving the equivalent non-linear model. Meanwhile, an optimized group decision-making portfolio strategy is established to better achieve the goal of increasing group decision-making investors' returns or reducing risks. Finally, numerical simulations are performed to find effective frontiers for future portfolio selection, which verifies the validity and feasibility of the models and methods proposed in this paper.