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

Abstract

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.