Hierarchical Sequential Three-Way Multi-Attribute Decision-Making Method Based on Regret Theory in Multi-Scale Fuzzy Decision Systems

Most of the existing multi-attribute decision-making models under multi-scale decision information systems are established by selecting the optimal scale or fusing multi-scale information into a single scale. These models will lose part of the decision information, resulting in inaccurate decision results. However, sequential three-way decision can not only process information hierarchically, but also provide delayed decision between acceptance and rejection. In addition, the irrational behavior of decision-makers will have a certain impact on the decision-making results. To this end, for multi-scale and diversity decision-making problems, this paper proposes a hierarchical sequential three-way multi-attribute decision-making method based on regret theory. Specifically, to represent this diversity, the multi-scale evaluation information table is converted into a digital evaluation value table through a fuzzy membership function. Second, based on the regret-rejoicing function of regret theory, the regret-rejoicing relation of alternatives in multi-scale information systems is established, which can be used to calculate conditional probability. Third, the relative loss functions based on regret theory are proposed by considering the psychological behaviors of decision-makers. Finally, the hierarchical sequential three-way multi-attribute decision-making method for solving the multi-scale decision-making problem is proposed. The stability and effectiveness of the proposed method are verified by the corresponding experiments and the comparative analysis of practical cases. The proposed method solves the fusion problem of multi-scale decision information and obtains flexible ranking results according to the risk factor.