Multi-parameter Portfolio Selection Model with Some Novel Score-Deviation Under Dual Hesitant Fuzzy Environment

Abstract

In risk investment, investors have to rely on uncertain information when it is difficult to obtain enough precise data. Dual hesitant fuzzy set (DHFS) is more applicable to deal with uncertain information because it involves membership degrees and non-membership degrees, which can validly describe positive and negative information, respectively. Although there has been research on decision-making based on the DHFS, the focus still remains on ranking the alternatives and choosing the best one, which cannot help investors to find the optimal portfolios. Therefore, to solve this problem, we mainly propose two novel portfolio selection models based on the DHFS in this paper. Firstly, we propose a Max-score dual hesitant fuzzy portfolio selection model with information preference (Model 3) for investors focusing on returns regardless of risks. Secondly, to consider the risks of portfolios, we improve Model 3 and develop a score-deviation dual hesitant fuzzy portfolio selection model with information preference and risk appetite (Model 5). Finally, a case study is conducted to highlight the effectiveness of the proposed models. A detailed sensitivity analysis and an efficient frontier analysis show that Model 5 can validly capture investors’ information preferences and risk appetites. Furthermore, compared with the hesitant fuzzy portfolio model, Model 5 can offer more options to the investors with different information preferences.