SF-GRA method based on cumulative prospect theory for multiple attribute group decision making and its application to emergency supplies supplier selection

Abstract

Emergency supplies supplier selection can be regarded as a classic multiple attribute group decision making (MAGDM) problem. MAGDM is an interesting everyday problem full of uncertainty and ambiguity. As a new extension of fuzzy sets (FSs), spherical fuzzy sets (SFSs) can express vague and complex information in MAGDM more comprehensively. The gray relational analysis (GRA) is a practical method to process MAGDM problems. Furthermore, the cumulative prospect theory (CPT) can well capture the psychological behaviors of decision makers (DMs) in the assessment process. Therefore, in this paper, a spherical fuzzy GRA based on CPT (SF-CPT-GRA) method is proposed for MAGDM issues. In the meantime, the CRiteria Importance Through Intercriteria Correlation (CRITIC) method is used under the spherical fuzzy environment to obtain unknown attribute weights, which enhances the rationality of weight information. Finally, an example of emergency supplies supplier selection is given to illustrate the practicality of the proposed method. Sensitivity analysis and further comparative analysis attest the stability and validity of SF-CPT-GRA method. The proposed method takes full account of the influence of DMs’ risk attitude on decision result, which integrates CPT with GRA (CPT-GRA) and uses SFSs to express DMs’ preference information, making the decision results more scientific. Moreover, the SF-CPT-GRA method provides some references for dealing with other complex uncertain problems and further extension of CPT-GRA method in other decision environments.