A novel approach to multi-attribute group decision-making: Optimistic and pessimistic three-state three-way decision models

The three-state three-way decision (TSTWD) model extends the classic three-way decision (TWD) model by incorporating an uncertainty state. To properly describe decision risks inherent in multi-attribute group decision-making (MAGDM) problem, this paper proposes a novel approach employing optimistic and pessimistic TSTWD models. Firstly, the optimistic and pessimistic TSTWD models are constructed to effectively capture the diverse attitudes of decision-makers (DMs) towards different decision-making scenarios. Secondly, the relative loss functions of the proposed two TSTWD models are derived based on the attribute evaluation values, respectively, and some properties of three threshold functions are discussed in detail. Thirdly, a framework to solve the MAGDM problem is developed based on proposed optimistic and pessimistic TSTWD models, in which the conditional probabilities with respect to the three states are calculated based on the positive ideal solution, negative ideal solution, and compromise solution, respectively. Simultaneously, a loss function aggregation method is presented to determine the comprehensive losses of alternatives. Finally, the feasibility and effectiveness of the proposed method are verified through illustrative examples, sensitivity as well as comparative analysis.