Group decision making based on the modified probability calculation method and DEA cross-efficiency with probabilistic hesitant fuzzy preference relations

Abstract

In this paper, we propose a novel group decision making (GDM) method with probabilistic hesitant fuzzy preference relations (PHFPRs) based on the modified probability calculation method and data envelopment analysis (DEA) cross-efficiency. The primary advantage of the method is that it can reduce information loss and ensure the reliability of the decision-making result. A modified probability calculation method for hesitant fuzzy preference relations (HFPRs) is first proposed to obtain complete and normalized PHFPRs. Then, for the consistent additive preference relation (APR), we construct an output-oriented DEA model to derive the priority vector, in which each alternative is regarded as a decision-making unit (DMU). A DEA cross-efficiency model is further proposed to yield the priority vector, irrespective of whether the desired consistency level is achieved. Furthermore, a stochastic analysis method is developed to obtain the expected priority vector for any PHFPR, and a mathematical programming model is established to obtain the weight vector of decision makers based on group consensus. Finally, the procedure of the GDM method based on the modified probability calculation and the DEA cross-efficiency is designed. We also show the applicability and effectiveness of the proposed GDM method using illustrative examples.