Abstract
An incomplete fuzzy preference framework for the Graph Model for Conflict Resolution (GMCR) is proposed to handle both complete and incomplete fuzzy preference information. Usually, decision makers’ (DMs’) fuzzy preferences are assumed to be complete fuzzy preference relations (FPRs). However, in real-life situations, due to lack of information or limited expertise in the problem domain, any DM’s preference may be an incomplete fuzzy preference relation (IFPR). An inherent advantage of the proposed framework for GMCR is that it can complete the IFPRs based on additive consistency, which is a special form of transitivity, a common property of preferences. After introducing the concepts of FPR, IFPR, and transitivity, we propose an algorithm to supplement IFPR, that is, to find an FPR that is a good approximation. To illustrate the usefulness of the incomplete fuzzy preference framework for GMCR, we demonstrate it using to a real-world conflict over water allocation that took place in the Zhanghe River basin of China.
Highlights
Strategic conflict is common in multiple-participant multiple-objective decision situations [1,2]
graph model for conflict resolution (GMCR) is a flexible methodology for systematically modeling and analyzing conflicts, with several advantages [11,12]: first, it can handle any finite number of decision makers (DMs), each of whom controls any finite number of options; second, it requires only DMs’ relative preferences over feasible states; third, it can deal with both transitive and intransitive preference information, and properly describe reversible and irreversible moves
We propose an algorithm to supplement incomplete fuzzy preference relation (IFPR) based on additive consistency
Summary
Strategic conflict is common in multiple-participant multiple-objective decision situations [1,2]. GMCR is a flexible methodology for systematically modeling and analyzing conflicts, with several advantages [11,12]: first, it can handle any finite number of DMs, each of whom controls any finite number of options; second, it requires only DMs’ relative preferences over feasible states; third, it can deal with both transitive and intransitive preference information, and properly describe reversible and irreversible moves. GMCR requires each DM’s relative preferences over the feasible states. To illustrate the usefulness of the incomplete fuzzy preference framework for GMCR, we apply it to a model of a real-world conflict, the water allocation conflict in the Zhanghe River basin (see [45]).
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