The graph model for conflict resolution with incomplete fuzzy reciprocal preference relations

Abstract

Within the paradigm of the Graph Model for Conflict Resolution (GMCR), fuzzy reciprocal preference relations (FPRs) can be usually employed to handle decision makers' (DMs') certain and uncertain preferences. Due to lack of time, limited expertise, or dynamic factors, the DMs' fuzzy preferences over the alternatives or states may be incomplete. Thus, a new preference relation, the incomplete fuzzy reciprocal preference relation (IFPR), is proposed to deal with both complete and incomplete fuzzy preferences within GMCR. In this study, one key contribution is that, according to DMs' attitude to risk associated with incomplete fuzzy preferences, four extended sets of stability definitions are put forward for providing a nuanced description of human behavior for both two-DM and n-DM conflict models. Furthermore, the interrelationships of solution concepts within and across the four extensions of stability definitions are investigated. Finally, an illustrative example, the potential large-scale export of water from Lake Gisborne, Canada, is used to show the usefulness of GMCR with incomplete fuzzy reciprocal preference relations.