Multi-criteria sequential three-state three-way decision consensus model based on set pair analysis theory

The three-way decision (3WD) theory involves two states of objects corresponding to consensus and conflict states in multi-criteria group decision-making (MCGDM) problems. However, the set pair analysis (SPA) theory provides a three-state perspective by incorporating the uncertainty state. Inspired of this, we propose a multi-criteria sequential three-state three-way decision (TS3WD) consensus model to reach the group consensus. Firstly, we propose the concept of consensus set pair probability space. Drawing upon SPA theory, the set pair consensus rules are designed to obtain the consensus set pair probability space which is categorized into three states including consensus, uncertainty and conflict. Secondly, the TS3WD model is presented by extending two states of classic 3WD model into three states. Related to the consensus set pair probability space and extended loss functions, the three-state decision rules and simplified decision rules are derived. Furthermore, the consensus feedback mechanism and rules based on the sequential TS3WD consensus model are proposed to adjust uncertainty and conflict opinions, in which the consensus adjustment model and coefficient adjustment strategy play essential roles. Finally, a connection number (CN) is applied to rank all alternatives and some experimental analyses are conducted to demonstrate the effectiveness and feasibility of the proposed model.