Belief Option Prioritization in the Graph Model for Conflict Resolution

In the graph model for conflict resolution (GMCR), option prioritization is an important approach to obtain preferences of decision makers (DMs) over a special conflict. The preference, based on ordered preference statements, is influenced by the authenticity and the order of preference statements. Owing to ambiguous evidence and incomplete information in complex real-world conflicts, it is of great difficulty to determine crisp preference over states for DMs. Some uncertain preferences have been introduced to cope with two situations that uncertain about preference statements authenticity or prioritization. The belief structure can be used to capture vagueness or unknown in subjective judgments. In this article, we propose a belief option prioritization technique by considering two situations of preference statements to elicit preferences comprehensively and efficiently. First, a belief structure is applied to describe the uncertainty of preference statement authenticity. The belief degree represents the accuracy of each preference statement and the real preference attitude of a DM. Second, a belief distribution, associated with an ordered sequence of preference statements, is used to capture the uncertainty on the prioritization of preference statements. The belief preference over feasible states can be obtained by the scoring scheme of option prioritization based on the ordered preference statements. Last, we propose an overall belief option prioritization technique by combining two uncertain situations. The application of Gisborne Lake water export conflict is utilized to illustrate the use of belief option prioritization.