Handling multi-granular hesitant information: A group decision-making method based on cross-efficiency with regret theory.

This paper presents a new method for group decision-making (GDM) under multi-granular hesitant information based on the data envelopment analysis (DEA) cross-efficiency approach with regret theory (MGDM-RCE), which addresses some limitations of classic DEA for hesitant linguistic information, such as ignoring decision-makers (DMs)’s non-rational behavior and the use of single-granularity scales. The proposed MGDM-RCE method, on the foundation of cross-efficiency and regret theory with multi-granular hesitant fuzzy linguistic term sets (HFLTSs), allows for constructing two cross-efficiency models based on total regret-rejoice utility values to determine cross-efficiency intervals of decision-making units (DMUs). Additionally, an extended stochastic cross-efficiency technique is developed for obtaining the final ranking of alternatives in the correlative GDM problem. The performance of the MGDM-RCE method is shown using a numerical example consisting of selecting new energy sources and its validity and superiority are analyzed through sensitivity and comparative analysis. The sensitivity analysis revealed that variations in the parameters of the MGDM-RCE method do not significantly affect the ranking results. Moreover, compared to the classic methods VIKOR and TOPSIS, the MGDM-RCE method exhibits higher stability characteristics in addressing the GDM problem.