Composite Decision Makers in the Graph Model for Conflict Resolution: Hesitant Fuzzy Preference Modeling

Abstract

Hesitant fuzzy preference relations (HFPRs) are formally proposed to model the conflict situation in which each decision maker (DM) consists of multiple individuals and each individual has its own fuzzy preferences over the feasible states within the framework of the graph model for conflict resolution (GMCR). Based on HFPRs, new definitions for hesitant fuzzy Nash stability, hesitant fuzzy general metarationality, hesitant fuzzy symmetric metarationality, and hesitant fuzzy sequential stability permit stability analyses to be carried out. Moreover, a new option prioritization technique, called hesitant fuzzy option prioritization, is developed for modeling a DM’s HFPRs based on the DM’s priority sequence of preference statements, the DM’s fuzzy truth values and levels of confidence. The groundwater contamination conflict of Elmira, Ontario, Canada, is utilized as a case study to illustrate the usefulness and applicability of the hesitant fuzzy option prioritization technique and GMCR with HFPRs.