The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio’s performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018.

中文翻译：

---

基于信用理论的投资组合优化多目标方法

本研究提出了一种新的方法来解决投资者在模糊背景下考虑不同投资标准所面临的问题。该方法将随机均值方差模型扩展到模糊多目标模型，其中除了回报和风险等常用指标外，还考虑流动性来量化投资组合的表现。未来收益的不确定性和潜在资产的未来流动性采用梯形模糊数建模。所提出方法的决策过程认为投资组合选择是一个多维问题，也是投资者应用的一些现实约束。特别是，这种方法优化了投资组合的预期回报、风险和预期流动性，同时考虑了边界约束和基数限制。因此，出现了约束组合的优化问题，该问题通过 NSGA-II 算法解决。本研究定义了用于选择最佳投资组合的可信 Sortino 比率和可信 STARR 比率。包括对 S&P100 指数的实证研究，以展示模型在实际应用中的表现。获得的结果表明，在 2008 年至 2018 年的分析期间，新方法在回报和风险方面可以超过该指数。包含 P100 指标以显示模型在实际应用中的性能。获得的结果表明，在 2008 年至 2018 年的分析期间，新方法在回报和风险方面可以超过该指数。包含 P100 指标以显示模型在实际应用中的性能。获得的结果表明，在 2008 年至 2018 年的分析期间，新方法在回报和风险方面可以超过该指数。