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.

Within the context of capability-based system-of-systems (SoS), the technology selection involves multiple stakeholders interactively participating in decision-making. In this article, a novel approach based on graph model for conflict resolution (GMCR) is proposed to handle the interactive technology selection decision across capability domains. First, a GMCR methodology based decision analysis framework for technology selection is presented, which allows decision-makers (DMs) with distinct risk attitudes, preference knowledge, and degrees of foresight to independently and interactively participate in technology selection. Then, the technology selection model is established by a four-step procedure that incorporates improved fuzzy option prioritization, followed by systematical technology selection analysis to provide strategic insights for identifying potential mutually accepted technology portfolios. Finally, an illustrative example is used to demonstrate the applicability and effectiveness of the proposed approach.

The hierarchical graph model for conflict resolution (HGMCR) serves as a powerful tool for analyzing multiple interrelated conflicts, in which decision makers (DMs) at different levels are brought together and assumed to have symmetrical power. In some hierarchical conflicts, however, the DMs may vary in power and influence the ultimate conflict resolution at diverse extents. Accordingly, this paper aims to introduce the power asymmetry into basic HGMCR (B HGMCR) to resolve more complex hierarchical conflict problems. Initially, power dynamics are defined to capture the preference relations of DMs under power asymmetry. Then, matrix-based BHGMCR modeling under power asymmetry is presented, followed by the expansion of four classic stability definitions. Finally, a case study on carbon emission conflict is used to demonstrate that the proposed approach can handle the real-world hierarchical conflicts. The intervention of government power can promote carbon reform in a global perspective.

When a conflict occurs, the disputants involved and interested third parties usually expect to reach the desired equilibrium. To achieve this goal, inverse graph model for conflict resolution is an effective way to make the state of interest an equilibrium by ascertaining the required preferences. However, specifying crisp cost or effort of changing preferences over states can be challenging for decision makers (DMs) and third parties. As a result, a new inverse preference optimization model using interval optimization is introduced into the graph model by considering the uncertain cost of preference adjustment. First, the preference adjustment cost with uncertainty is formulated using interval number. Then, pessimistic preference ordering and DMs’ degrees of risk tolerance are utilized to compare cost intervals. After that, an inverse preference optimization model with uncertain adjustment cost is established. Finally, an illustrative example of the bulk water export conflict in Canada is presented to demonstrate the feasibility and effectiveness of the proposed approach.

A belief-based preference structure along with its associated elicitation approach is incorporated into the graph model for conflict resolution (GMCR) to model and analyze the multistakeholder strategic conflicts involving ambiguous evidences, incomplete information, and nonlinear causal relationships. More specifically, the relative preference is first redefined using a belief structure capable of capturing uncertainties of various types such as vagueness and/or ignorance in subjective judgments regarding the complex real-world conflicts. Next, a flexible and realistic methodology based on evidential reasoning is put forward to elicit the belief preference information over feasible states within the GMCR model. Then, 16 stability definitions (solution concepts) are extended to accommodate diverse uncertainties in preferences and facilitate the informed conflict analysis. The application and interpretation of the foregoing preference structure and associated stability definitions are demonstrated with an illustrative example.

A novel approach based on genetic algorithm (GA) is put forward to determine the possible relative preference required to reach the desired equilibria for the focal decision-makers (DMs) or the third party from the inverse perspective. More specifically, a framework of inverse graph model for conflict resolution (GMCR) modified from original GMCR incorporating GA's procedure is proposed to provide DMs with strategic insights toward inverse problems with conflict resolution. By taking full advantage of the optimization and search capability of GA, an improved preference calculation method is developed to help DMs focus limited resources on visionary strategies. Finally, an illustrative example is applied to demonstrate the applicability of the proposed approach in practice.