Graph model for multiple composite decision makers with large-scale groups: Probability-hesitant fuzzy preference modeling and application

Whenever humans interact with others, conflict inevitably arises. Sometimes, multiple composite decision makers (CDMs) are involved, some of which may be large-scale groups. When making a decision or strategy selection, a CDM needs to consider the interests of the group and the wishes of individual decision makers (IDMs). For example, a CDM may judge a move to be an improvement only if a certain fraction of IDMs consider it so – in other words, only when the IDMs reach a certain degree of consensus. This paper proposes an index of group consensus on more preferred (IGCMP) and an index of group consensus on less preferred (IGCLP), and uses them to determine whether a CDM more or less prefers the current state to another and reflect the heterogeneous characteristics of CDMs, including conservative, aggressive, and eclectic. Accordingly, the conflict for multiple CDMs with large-scale groups is investigated in this paper from the perspective of group consensus within the framework of the Graph Model for Conflict Resolution (GMCR). At first, CDMs’ preferences are represented by probability-hesitant fuzzy preference relations, which can reflect the heterogeneity of IDMs and preference uncertainty of CDMs. Then, the new forms of the unilateral improvement list for CDMs and coalitions are developed based on IGCMP and IGCLP. Subsequently, five extended stability definitions and their relationships are studied. Finally, to demonstrate the effectiveness of the new method, it is applied to model a water pollution conflict in the Yangtze River Delta, China.