Hesitant fuzzy portfolio selection model with score and novel hesitant semi-variance

Abstract

Because of the effectiveness in describing uncertain information, the hesitant fuzzy set (HFS) has been well applied in decision making and portfolio selection. Although there have been some risk measures based on the HFS, most of them consider all the membership degrees in the calculation. In fact, investors usually think that only the low membership degrees are undesirable, but this fact is ignored by some researchers in the existing hesitant fuzzy portfolio selection models. Therefore, to better capture investors’ risk attitudes, we extend the downside risk from stochastic environment to hesitant fuzzy environment and define a new hesitant semi-variance (HSV). Then, the corresponding theoretical analysis on the novel definitions is given by strictly mathematical deduction. Moreover, two new score-HSV portfolio selection models are proposed, in which the portfolio return is measured by the score, whereas the risk is measured by the HSV instead of deviation. The two new models can avoid neglecting the portfolios with distinctly high membership degrees, which are desirable for investors in practice. Finally, a case study is provided to illustrate the effectiveness of these models. Sensitivity analysis implies that results of the models are consistent with investors’ preferences for assets.