Interval fuzzy preferences in the graph model for conflict resolution

On some properties of limited move stability, generalized metarationality, and policy equilibrium in bilateral conflicts

Conflict of environmental sustainable development as a common phenomenon can be seen everywhere in life. To capture consensus problems of decision makers (DMs) in conflict, a consensus and non-consensus fuzzy preference relation (FPR) matrix is proposed to the framework of the Graph Model for Conflict Resolution (GMCR). Concentrating on the case of two DMs within GMCR paradigm, four standard fuzzy solution concepts are developed into eight fuzzy stability definitions which can fully represent DMs’ behavior characteristics of win-win and self-interested. To demonstrate how the novel GMCR methodology proposed in this paper can be conveniently utilized in practice, it is then applied to an environmental sustainable development conflict with two DMs. The results show that the general fuzzy equilibrium solutions are the intersection of consensus fuzzy equilibrium and non-consensus fuzzy equilibrium. Therefore, the GMCR technique considering DMs’ consensus can effectively predict the various possible solutions of conflict development under different DMs’ behavior preferences and provide new insights for analysts into a conflict.

A hybrid preference framework is proposed for strategic conflict analysis to integrate preference strength and preference uncertainty into the paradigm of the graph model for conflict resolution (GMCR) under multiple decision makers. This structure offers decision makers a more flexible mechanism for preference expression, which can include strong or mild preference of one state or scenario over another, as well as equal preference. In addition, preference between two states can be uncertain. The result is a preference framework that is more general than existing models which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, four kinds of stability are defined as solution concepts and a post-stability analysis, called status quo analysis, which can be used to track the evolution of a given conflict. Algorithms are provided for implementing the key inputs of stability analysis and status quo analysis within the extended preference structure. The new stability concepts under the hybrid preference structure can be used to model complex strategic conflicts arising in practical applications, and can provide new insights for the conflicts. The method is illustrated using the conflict over proposed bulk water exports from Lake Gisborne in Newfoundland, Canada.

This paper proposes a new algebraic definition that facilities calculating of Stackelberg stability in a graph model for conflict resolution with two decision makers. Most stability definitions used in the graph model methodology place decision makers at the same level, in the sense that their roles are symmetric. In practice, however, one decision maker may join by forcing the other to respond to his or her decision. So, to be applied, a model must specify the leader and the follower. Stackelberg stability can be defined logically, but an algorithm to implement it has not been developed until now, due to its complicated recursive formula. To permit Stackelberg stability to be calculated efficiently and encoded conveniently, within a decision support system, an algebraic test for the stability is developed. This algebraic representation of Stackelberg stability is easy to implement and interpret. A superpower military confrontation is used to illustrate how Stackelberg stability can be employed to a real-world application using the new approach.KeywordsConflict analysisDecision makerAlgebraic expressionsStackelberg stabilityGraph modelOrdinal preferences

Conflict Analysis is a set of techniques to model and analyze a strategic conflict, or policy problem, using models of the purposive behavior of actors. After a review of these methods, the Graph Model for Conflict Resolution, which stands out for the flexibility of its models and the breadth of its analysis, is described in detail. After an historical overview, its development is compared to other Conflict Analysis techniques, including Drama Theory (See the chapter by Bryant, this volume), and to the Non-cooperative Game Theory (Chatterjee, in this volume) that inspired them. The graph model system is prescriptive, aiming to provide a specific decision-maker with relevant and insightful strategic advice. The capacity of the graph model to generate useful advice is emphasized throughout, and illustrated using a real-life groundwater contamination dispute. The description of the graph model includes the basic modeling and analysis components of the methodology and the decision support system GMCR II that has been used to apply it, including both basic (stability) analysis and follow-up analysis. New developments ensure that the next generation of decision support based on the graph model will be much more comprehensive and powerful.

Conflict is an inevitable social phenomenon and the analysis of it can effectively resolve disputes, improve the position of decision makers (DMs), forecast compromise solutions as well. At present, the Graph Model for Conflict Resolution (GMCR), a completely non-quantitative decision support system (DSS) based on DM’s ordinal preference information, is constructed to combat conflict analysis complicated by multiple participant or multiple criteria or both. The purpose of the study is to introduce an overview of GMCR in conflict analyzing through bibliometrics. In order to achieve this goal, a systematic review of articles in leading journals of Web of Science Core Collection (WoSCC) during 1987–2019 is posed, referring to the distribution of countries, institutions, authors, subjects and journals, research topics and hotspots exploration as well as frontiers prediction, by utilizing VOSviewer and CiteSpace. The contributions of this study are not only providing a handy method to grasp generalized scientific research situation, but also demonstrating status quo and emerging trends of GMCR for researchers and everyone who interested in.

Many solution concepts have been proposed within the Graph Model for Conflict Resolution to represent many behaviors that decision makers (DMs) can have in strategic settings. Among these solution concepts, the limited move stability stands out because it allows analyzing the conflict a variable number of steps forward, taking into account the preferences of all DMs involved in the conflict. However, for conflicts involving more than two DMs, there are two definitions of limited move stability that we argue to have undesired properties. For that reason, we present two alternative definitions for limited move stability for conflicts with multiple DMs, called: Alternative Limited-Move stability with Cooperative Coalition ( $$L_h^{CC}$$ ) and Alternative Limited-Move stability with Individualistic Coalition ( $$L_h^{CI}$$ ). Moreover, we obtained results relating these concepts to classical GMCR stability concepts. Furthermore, we provide results that establish the equivalence among the stability notions $$L_h^{CC}$$ , $$L_h^{CI}$$ and $$\text {Maximin}_h$$ , for conflicts in which the DMs belonging to the opposing coalition have equal and completely opposite preferences to those of the focal DM. An application to the Elmira conflict illustrates the usefulness of the proposed concepts in a real conflict situation.

We present a generalization of the graph model for conflict resolution, introducing the possibility of decision makers (DMs) expressing their preferences among the possible scenarios through probabilistic preferences. In this new scenario, four stability definitions (solution concepts) are proposed: 1) α-Nash stability; 2) (α, β)-metarationality; 3) (α, β)-symmetric metarationality; and 4) (α, β, γ)-sequential stability. We deal with conflicts that involve two or more DMs. Relationships between these definitions are demonstrated, as well as an analysis of how the values of the parameters α, β, and y influence the set of stable states is made. Applications of the proposed model to conflicts involving two and three DMs are presented. The analysis of these applications highlights the advantages gained by allowing individuals to express their preferences probabilistically.

The graph model for conflict resolution (GMCR), along with its associated decision support system GMCR II, is employed for systematically studying the strategic aspects of a conflict existing in Per Aru basin. National Water Supply & Drainage Board has planned to build a reservoir on the Per Aru for the sole purpose of supplying drinking water to the urban areas of Vavuniya district. People who will be affected due to the inundation of their lands have shown resistance to the construction of the reservoir. Moreover, government organizations such as Forest Department and Wildlife Department also have expressed their concerns over the construction of a reservoir since that will have diverse impacts on forest lands and wildlife in the area that will be inundated by the proposed reservoir. The above three stakeholders, viz., National Water Supply & Drainage Board, affected people and government organizations suggest a few options to solve the conflict.The options are specific actions that can actually occur in a conflict. The decision support system, GMCR II, was used to investigate and resolve this conflict. The paper presents all the steps involved in the modeling of the conflict using GMCR II and analysis of the results obtained from the model. The National Water Supply & Drainage Board accepting to reduce the inundation area and agreeing to release sufficient environmental flow was resulted as the best possible solution acceptable for all the three parties.The solution includes affected people and Government Organizations agreeing for the construction of the reservoir at the original location. ENGINEER, Vol. 47, No. 03, pp. 61-70, 2014

In this paper, status quo analysis is addressed by using both logical and matrix representations in the graph model with strength of preference. The graph model for conflict resolution (GMCR) provides a convenient and effective means to model and analyze a strategic conflict. The graph model has entertained diverse preference structures to characterize decision-makers' (DMs) preference over feasible states, including simple preference, preference uncertainty, and strength of preference. The ¿simple preference¿ structure consists of a strict preference relation and an indifference relation to represent a DM's preference for one state relative to another. Another ¿strength of preference¿ framework allows a DM to express its strong or mild preference for one state over another, as well as the indifference relation. When a graph model is established for a strategic conflict, the standard practice is to carry out a stability analysis first, and then, followed by a post-stability analysis such as coalition analysis and status quo analysis. Status quo analysis complements stability analysis and aims at assessing whether predicted equilibria are attainable from the status quo. So far, status quo analysis has been examined for the graph model with simple preference and both logical and matrix representations of status quo analysis have been developed. This article extends these results to handle status quo analysis for the graph model with strength of preference. The algebraic method is illustrated using a conflict over proposed bulk water exports from Lake Gisborne in Newfoundland.

A novel two-level hierarchical graph model is developed to analyze international climate change negotiations with hierarchical structures: the negotiations take place between two nations and between each nation and its provincial governments. The two national government are two decision makers at the top level. Within each nation, the two provincial governments negotiate with the national government at the lower level. The theoretical structure of this novel model, including decision makers, options, moves, and preference relations, are developed. The interrelationship between the stabilities in the two-level hierarchical graph model and the stabilities in local models are investigated by theorems. These theorems can be utilized to calculate complete stabilities in the two-level hierarchical graph model when the stabilities in local graph models are known. The international climate change negotiations as the illustrative example is then investigated in detail. The extra equilibrium, uniquely obtained by this novel methodology, suggests that opposition may still be from one provincial government when the national government does not sign the international climate agreement and implements existing environmental laws. Compared with other approaches, this novel methodology is an effective and flexible tool in analyzing hierarchical conflicts at two levels by providing decision makers with strategic resolutions with broader vision.

To demonstrate the strategic influence a third party can have on negotiations, a formal approach to resolving a complex conflict is applied to an important international water resources controversy. Specifically, third party intervention is employed within the framework of the Graph Model for Conflict Resolution (GMCR) to systematically investigate the ongoing dispute between Bangladesh and India over the regulation of the Ganges River by India at the Farakka Barrage located just upstream on the Ganges River in India before it flows into Bangladesh. A general system of systems engineering approach to Third Party Intervention within the GMCR structure is designed to reflect a range of ways in which it can be implemented in practice. Having an insightful and powerful tool like Third Party GMCR permits one to ascertain how a Third Party can guide a serious conflict to a more reasonable resolution which may be mutually beneficial to all concerned parties.

An option prioritization technique is developed to efficiently elicit the preferences, both unknown and crisp, of decision makers (DMs) in strategic conflicts. In the Graph Model for Conflict Resolution, each DM has one or more options, each of which may be selected or not. A state, or possible scenario, is formed when all DMs make an option selection. The software GMCR II contains an option prioritization procedure that makes it easy for a modeller to enter a DM’s crisp preference ordering over the states using prioritized statements describing the DM’s preferred option combinations. This procedure is extended by adding two new logical connectives that describe uncertainty of preference. For each DM, a range of possible scores for each feasible state can then be calculated, facilitating the determination of a preference ordering containing uncertainty by comparing and ranking scores. To demonstrate how this new methodology can be used to represent unknown preferences in a real-world decision problem, it is applied to a Canadian dispute over proposed water exports.

This research examines how third parties recognize bias blind spots in business decision-making by using matrix-based graph models. We use the mathematical, theoretical, and philosophical foundations of the Graph Model for Conflict Resolution to emphasize the significance of recognition of bias blind spots as a means to enhance informed decision-making. We introduce the Bias Blind Spots Graph Model and provide a mathematical framework for modeling bias blind spots. Additionally, we provide evidence of the effectiveness of accounting for the presence of bias blind spots that influence decision-making within the context of Japan’s Skymark Airlines . In showcasing the theoretical underpinnings and practical applicability of this model, we contribute to identifying bias blind spots in reasoning and judgment. Further, we extend the model by providing mathematical foundations for considering decision-maker preference and outcome state stability/equilibrium. Ultimately, our findings offer valuable insights for both researchers and third parties to model and evaluate the influences of cognitive bias blind spots in decision-making processes in organizational settings.

Third-party mediation has been proved to be an effective way to resolve conflicts. T he p reference optimization based on inverse Graph Model for Conflict Resolution (GMCR) provides strong theoretical support for the formulation of a third-party mediation scheme. Real-world conflict parties have complicated preferences, which may or may not be transferred. In order to determine an optimal preference under the desired equilibrium, this work considers the conditions of transitive preferences into the current preference optimization model based on inverse GMCR. Only non-transmitted preferences have been examined in the current inverse preference research. Due to its intuitiveness, Directed Acyclic Giagram (DAG) is utilized to express the transitive preference structure in order to more accurately represent preference. The desired preference is then searched for across a large number of preference profiles by using a Genetic Algorithm-based approach. Double genes are designed: permutation gene and connected gene make up the, which is successful to solve the problem. These two genes can be converted to decision-maker's (DM's) preference matrix by specific permutations a nd transformations. Finally, a case of water resource conflict i s used to verify 0 ur work's rationality and practical significance.