Cross-Efficiency Evaluation under Probabilistic Hesitant Fuzzy Environment and Its Application to the Portfolio Selection Process

In the case of insufficient quantitative data, qualitative evaluation information is very important for investment decision-making. However, if it is completely based on qualitative evaluation information, the results may be subjective. In response to this problem, this paper proposes a method, namely, probabilistic hesitant fuzzy cross-efficiency evaluation (PHFCEE) method, based on probabilistic hesitant fuzzy theory, cross-efficiency data envelopment analysis (CEDEA). This method uses probabilistic hesitant fuzzy sets to collect qualitative evaluation information and then uses the cross-efficiency DEA model to fuse quantitative data and qualitative information. And finally, an investment portfolio is built based on the cross-efficiency value and its variance. In addition, this article gives the specific operating steps of the PHFCEE method and uses the construction of a portfolio of 10 stocks in the China CSI 300 Index as an example to illustrate the effectiveness of this method.

CPT-MABAC-Based multiple attribute group decision making method with probabilistic hesitant fuzzy information

Facing with a sea of fuzzy information, decision makers always feel it difficult to select the optimal alternatives. Probabilistic hesitant fuzzy sets (PHFs) utilize the possible numbers and the possible membership degrees to describe the behavior of the decision makers. though this environment has been introduced to solve problems using different methods, this circumstance can still be explored by using different method. This paper’ s aim is to develop the MABAC (Multi-Attributive Border Approximation area Comparison) decision-making method which based on cumulative prospect theory (CPT) in probabilistic hesitant fuzzy environment to handle multiple attributes group decision making (MAGDM) problems. Then the weighting vector of attributes can be calculated by the method of entropy. Then, in order to show the applicability of the proposed method, it is validated by a case study for buying a house. Finally, through comparing the outcome of comparative analysis, we conclude that this designed method is acceptable.