A spherical Z-number multi-attribute group decision making model based on the prospect theory and GLDS method

Multi-attribute group decision-making is an important research field in decision science, and its theories and methods have been widely applied to engineering, economics and management. However, as the information embedded volume and complexity of decision-making expand, the diversity and heterogeneity of decision-making groups present significant challenges to the decision-making process. In order to effectively address these challenges, this paper defines the concept of spherical Z-number, which is a fuzzy number that takes into account a wide range of evaluation and its reliability. Additionally, a group decision-making model in a spherical Z-number environment is proposed. First, an objective phased tracking method is used to determine expert weights, maintain the consistency in decision-making group evaluations. The gained and lost dominance score method is combined with prospect theory to integrate expert psychological behavior when facing risks. The proposed method considers both group utility and individual regret, and balances the gains and losses of various options in the decision-making process. Finally, in response to the 3R principle, the model is employed to address the shared e-bike recycling supplier selection problem and to assess the viability of the decision-making outcomes. The results demonstrate that the model is robust in the context of varying parameter configurations. Moreover, the correlation coefficients between its ranking outcomes and those of alternative methodologies are all above 0.77, and its average superiority degree is 1.121, which is considerably higher than that of other methods. Consequently, the model's effectiveness and superiority are substantiated.