Three-way group decision-making based on geometric Heronian mean operators with q-Rung orthopair uncertain linguistic information

Abstract As an effective tool for three-way decisions (3WD) problems, decision-theoretic rough sets (DTRSs) have raised increasing attention recently. In view of the advantages of q‐rung orthopair uncertain linguistic variables ( q-OULVs) in depicting uncertain information, a new DTRSs model based on q -ROULVs is proposed to solve three-way group decision-making (3WGDM) problems. Firstly, the loss function of DTRSs is defined by q‐ROULVs and a q ‐rung orthopair uncertain linguistic DTRSs model is constructed. Secondly, to aggregate different experts’ evaluation results on loss function in group decision-making (GDM) scenario, the q‐rung orthopair uncertain linguistic geometric Heronian mean ( q‐ROULGHM ) operator and the q‐rung orthopair uncertain linguistic weighted geometric Heronian mean ( q‐ROULWGHM ) operator are presented. Related properties of the proposed operators are investigated. Thirdly, to compare the expected loss of each alternative, a new score function of q‐ROULVs is defined and the corresponding decision rules for 3WGDM are deduced. Finally, a descriptive example of venture capital in high-tech projects is provided to verify the rationality and effectiveness of our method. The influence of different conditional probabilities and parameter values on decision results is comprehensively discussed.