The resolution of real-world conflicts is often supported by third-party intervention (i.e., mediation). This paper proposes a possible mediation support in the form of a reverse optimization procedure under the framework of the Graph Model for Conflict Resolution (GMCR). The approach computes minimal priority adjustments of preference statements that are necessary to achieve a desired agreement. A mathematical model, based on the matrix form of GMCR, is developed to analyze this third-party mediation problem. Thereby, this study makes a first attempt to obtain option-based mediation strategies, which add comprehensiveness to the traditional state-based strategies, yet are easier to understand and hence more acceptable to the conflict participants. To illustrate the practicality, the proposed procedure is applied to a medical dispute between a patient and a hospital, with the aim to suggest changes in the ordering of preference statements that lead to a desired outcome.

Dempster-Shafer Theory (DST) and the Analytic Hierarchy Process (AHP) are integrated in order to elicit preference information from experts regarding decision makers (DMs) involved in a regulatory conflict. More precisely, DST is used for combining expert knowledge regarding preferences of a specific DM(the regulatory body), and AHP is employed for ranking feasible states in the conflict for this same DM. In order to illustrate how this preference elicitation proposal can be conveniently implemented in practice within the Graph Model for Conflict Resolution (GMCR), it is applied to a real construction dispute located in the city of Ipojuca, Brazil. The conflict is modeled with three DMs: support, opposition, and the regulatory body. Results show that the new preference methodology possesses many inherent advantages including high flexibility, the ability to capture uncertainty or even ignorance about preferences, the possibility of combining expert knowledge with respect to missing preferences, and a substantial reduction in the number of pairwise comparisons of states required to express preference information.

The strategic decisions and resulting consequences surrounding the conflict between the United States of America (US) and Iran regarding the Iranian nuclear program are formally investigated using a flexible decision methodology called the Graph Model for Conflict Resolution (GMCR). This highly controversial dispute caught the world’s attention as concerns were growing that Iran would reach a position where it would be able to build nuclear weapons, thereby posing a risk to world security. While Iran insisted on its rights for the peaceful use of nuclear technology, the international community, led by the US, tried to discourage the nuclear activities of Iran to ensure its obligations to the non-proliferation of nuclear weapons. This led to an escalation of tension on both sides, with an extension of the nuclear program by Iran and an increase in sanctions by the US, before it was possible to arrive at a negotiated agreement. As demonstrated in this paper, a systematic GMCR investigation provides valuable strategic insights into this important conflict. Further, it illustrates ways in which the conflict could have evolved, as well as mechanisms for stopping an escalation like this in the future.

This paper investigates the strategic cooperation of two competitive suppliers with different abilities and a weak main manufacturer in Complex Products Systems (CoPS), where a main manufacturer signs a revenue-sharing contract based on a relationship-specific investment with the stronger supplier. The stronger supplier provides one key element to the main manufacturer and encroaches on the downstream market by producing substitutable final products simultaneously. We consider multi-period decisions, by building different models based on centralized, decentralized, and cooperative decisions. The equilibrium strategies are characterized under downstream competition, and optimal cooperation strategies are derived by building multi-period game models. The results show that strong cooperation can enhance the economic performance of each individual as well as the whole supply chain. The weak main manufacturer would face the risk of strong suppliers’ supply interruptions when the competitive degree of suppliers and downstream competition are fierce enough under decentralized decisions. Additionally, the gap in the abilities of the two competitive suppliers reduces the main manufacturer’s profitability. However, the revenue-sharing contract based on a relationship-specific investment can motivate the strong supplier to establish cooperation relationship and improve both stakeholders’ profitability. Moreover, strategic cooperation is efficient to prevent the strong supplier encroaching on downstream and has a positive impact on boosting the weak main manufacturer’s market share. Meanwhile, nurturing a domestic supplier is an effective measure for improving competitiveness and indigenous technological capability of the main manufacturer in CoPS. Finally, some useful management sights on cooperation strategy and optimal decisions are derived.

Strategic resource allocation into decision-making model plays a valuable role for the defender in mitigating damage and improving efficiency in military environments. In this paper, we develop a defensive resource allocation model based on cumulative prospect theory (CPT), which considers terrorists’ psychological factors of decision-making in reality. More specifically, we extend existing models in the presence of multiple attributes and terrorists’ deviations from rationality using a multi-attribute cumulative prospect theory. In addition, interval values are used to cope with uncertainties regarding gain and loss. Comparative studies are also carried out to demonstrate the differences among minmax, Nash eguilibrium (NE), and traditional probability risk analysis (PRA) strategies. Results show that the defender’s optimal defensive resource allocation will change along with terrorists’ behaviors and the proposed model makes more sense compared with other traditional resource allocation strategies.

When people express their opinions for an issue, they can express both exact opinions and uncertain opinions, such as numerical interval opinions. Moreover, social network is a crucial medium of opinion interaction and evolution. In this paper, uncertain opinion evolution with bounded confidence effects in social networks is investigated by theoretical demonstration and numerical examples analyses, and experiments simulations analyses. Theoretical results show when all the agents are with uncertainty tolerances, then the ratios of agents expressing uncertain opinions are impossible to decrease, even increase, as time increases; while when all the agents are without uncertainty tolerances, then the ratios of agents expressing uncertain opinions are impossible to increase, even decrease, as time increases. Moreover, the average widths of uncertain opinions are always smaller than the maximum opinion width of all the initial opinions among agents. Experiments simulations results show different ratios of agents with uncertainty tolerances and different ratios of agents expressing uncertain opinions have strong impact on the ratios of the agents expressing the uncertain opinions in the stable state, and the average widths of uncertain opinions in the stable state.

The uncertainty distribution can more effectively express the uncertainty of decision makers’ judgments during a pairwise comparison of any alternatives. This paper investigates the priority models of group intuitionistic fuzzy preference relations with normal uncertainty distribution. The mathematical equivalence between the membership, non-membership degree interval fuzzy preference relation and the intuitionistic fuzzy preference relation is constructed, showing that there exists an inverse relationship between the priority of alternatives using these two types of interval preference relations. The new optimal models regarded the event that the deviation between the ideal judgement meeting the multiplicative consistency and the actual judgement obeying normal uncertainty distribution shall not exceed a threshold value under the given belief degree as a constraint, and regarded the minimum sum of all the threshold values as the objective function. The chance constraint was introduced to measure the degree to which multiplicative consistency can be realized under different belief degrees. The priority model provides a new method for simulating uncertainty and fuzziness in the real-world decision making environment.