Fuzzy Preferences in the Graph Model for Conflict Resolution

A Fuzzy Preference Framework for the Graph Model for Conflict Resolution (FGM) is developed so that real-world conflicts in which decision makers (DMs) have uncertain preferences can be modeled and analyzed mathematically in order to gain strategic insights. The graph model methodology constitutes both a formal representation of a multiple participant-multiple objective decision problem and a set of analysis procedures that provide insights into them. Because crisp or definite preference is a special case of fuzzy preference, the new framework of the graph model can include---and integrate into the analysis---both certain and uncertain information about DMs' preferences. In this sense, the FGM is an important generalization of the existing graph model for conflict resolution. One key contribution of this study is to extend the four basic graph model stability definitions to models with fuzzy preferences. Together, fuzzy Nash stability, fuzzy general metarationality, fuzzy symmetric metarationality, and fuzzy sequential stability provide a realistic description of human behavior under conflict in the face of uncertainty. A state is fuzzy stable for a DM if a move to any other state is not sufficiently likely to yield an outcome the DM prefers, where sufficiency is measured according to a fuzzy satisficing threshold that is characteristic of the DM. A fuzzy equilibrium, an outcome that is fuzzy stable for all DMs, therefore represents a possible resolution of the conflict. To demonstrate their applicability, the fuzzy stability definitions are applied to a generic two-DM sustainable development conflict, in which a developer plans to build or operate a project inspected by an environmental agency. This application identifies stable outcomes, and thus clarifies the necessary conditions for sustainability. The methodology is then applied to an actual dispute with more than two DMs concerning groundwater contamination that took place in Elmira, Ontario, Canada, again uncovering valuable strategic insights. To investigate how DMs with fuzzy preferences can cooperate in a strategic conflict, coalition fuzzy stability concepts are developed within FGM. In particular, coalition fuzzy Nash stability, coalition fuzzy general metarationality, coalition fuzzy symmetric metarationality, and coalition fuzzy sequential stability are defined, for both a coalition and a single DM. These concepts constitute a natural generalization of the corresponding non-cooperative fuzzy preference-based definitions for Nash stability, general metarationality, symmetric metarationality, and sequential stability, respectively. As a follow-up analysis of the non-cooperative fuzzy stability results and to demonstrate their applicability, the coalition fuzzy stability definitions are applied to the aforementioned Elmira groundwater contamination conflict. These new concepts can be conveniently utilized in the study of practical problems in order to gain strategic insights and to compare conclusions derived from both cooperative and non-cooperative stability notions. A fuzzy option prioritization technique is developed within the FGM so that uncertain preferences of DMs in strategic conflicts can be efficiently modeled as fuzzy preferences by using the fuzzy truth values they assign to preference statements about feasible states. The preference statements of a DM express desirable combinations of options or courses of action, and are listed in order of importance. A fuzzy truth value is a truth degree, expressed as a number between 0 and 1, capturing uncertainty in the truth of a preference statement at a feasible state. It is established that the output of a fuzzy preference formula, developed based on the fuzzy truth values of preference statements, is always a fuzzy preference relation. The fuzzy option prioritization methodology can also be employed when the truth values of preference statements at feasible states are formally based on Boolean logic, thereby generating a crisp preference over feasible states that is the same as would be found using the existing crisp option prioritization approach. Therefore, crisp option prioritization is a special case of fuzzy option prioritization. To demonstrate how this methodology can be used to represent fuzzy preferences in real-world problems, the new fuzzy option prioritization technique is applied to the Elmira aquifer contamination conflict. It is observed that the fuzzy preferences obtained by employing this technique are very close to those found using the rather complicated and tedious pairwise comparison approach

Preference Elicitation in the Graph Model for Conflict Resolution

Flexible approaches for eliciting preferences of decision makers involved in a conflict are developed along with applications to real-world disputes. More specifically, two multiple criteria decision making approaches are proposed for capturing the relative preferences of a decision maker participating in a conflict situation. A case study in logistics concerned with the conflict arising over the expansion of port facilities on the west coast of North America as well as a transportation negotiation dispute are used to illustrate how these approaches can be integrated with the Graph Model for Conflict Resolution, a practical conflict analysis methodology. Ascertaining the preferences of the decision makers taking part in a conflict constitutes a key element in the construction of a formal conflict model. In practice, the relative preferences, which reflect each decision maker’s objectives or goals in a given situation, are rather difficult to obtain. The first method for preference elicitation is to integrate an Analytic Hierarchy Process (AHP) preference ranking method with the Graph Model for Conflict Resolution. The AHP approach is used to elicit relative preferences of decision makers, and this preference information is then fed into a graph model for further stability analyses. The case study of the Canadian west coast port congestion conflict is investigated using this integrated model. Another approach is based on a fuzzy multiple criteria out-ranking technique called ELECTRE III. It is also employed for ranking states or possible scenarios in a conflict from most to least preferred, with ties allowed, by the decision maker according to his or her own value system. The model is applied to a transportation negotiation dispute between the two key parties consisting of shippers and carriers

Preference Uncertainty and Trust in Decision Making

A fuzzy approach for handling uncertain preferences is developed within the paradigm of the Graph Model for Conflict Resolution and new advances in trust modeling and assessment are put forward for permitting decision makers (DMs) to decide with whom to cooperate and trust in order to move from a potential resolution to a more preferred one that is not attainable on an individual basis. The applicability and the usefulness of the fuzzy preference and trust research for giving an enhanced strategic understanding about a dispute and its possible resolution are demonstrated by employing a realworld environmental conflict as well as two generic games that represent a wide range of real life encounters dealing with trust and cooperation dilemmas. The introduction of the uncertain preference representation extends the applicability of the Graph Model for Conflict Resolution to handle conflicts with missing or incomplete preference information. Assessing the presence of trust will help to compensate for the missing information and bridge the gap between a desired outcome and a feared betrayal. These advances in the areas of uncertain preferences and trust have potential applications in engineering decision making, electronic commerce, multiagent systems, international trade and many other areas where conflict is present. In order to model a conflict, it is assumed that the decision makers, options, and the preferences of the decision makers over possible states are known. However, it is often the case that the preferences are not known for certain. This could be due to lack of information, impreciseness, or misinformation intentionally supplied by a competitor. Fuzzy logic is applied to handle this type of information. In particular, it allows a decision maker to express preferences using linguistic terms rather than exact values. It also makes use of data intervals rather than crisp values which could accommodate minor shifts in values without drastically changing the overall results. The four solution concepts of Nash, general metarationality, symmetric metarationality, and sequential stability for determining stability and potential resolutions to a conflict, are extended to accommodate the new fuzzy preference representation. The newly proposed solution concepts are designed to work for two and more than two decision maker cases. Hypothetical and real life conflicts are used to demonstrate the applicability of this newly proposed procedure. Upon reaching a conflict resolution, it might be in the best interests of some of the decision makers to cooperate and form a coalition to move from the current resolution to a better one that is not achievable on an individual basis. This may require moving to an intermediate state or states which may be less preferred by some of the coalition members while being more preferred by others compared to the original or the final state. When the move is irreversible, which is the case in most real life situations, this requires the existence of a minimum level of trust to remove any fears of betrayal. The development of trust modeling and assessment techniques, allows decision makers to decide with whom to cooperate and trust. Illustrative examples are developed to show how this modeling works in practice. The new theoretical developments presented in this research enhance the applicability of the Graph Model for Conflict Resolution. The proposed trust modeling allows a reasonable way of analyzing and predicting the formation of coalitions in conflict analysis and cooperative game theory. It also opens doors for further research and developments in trust modeling in areas such as electronic commerce and multiagent systems

Status Quo Analysis of the Flathead River Conflict

Status quo analysis algorithms developed within the paradigm of the graph model for conflict resolution are applied to an international river basin conflict involving the United States and Canada to assess the likeliness of various compromise resolutions. The conflict arose because the state of Montana feared that further expansion of the Sage Creek Coal Company facilities in Canada would pollute the Flathead River, which flows from British Columbia into Montana. Significant insights not generally available from a static stability analysis are obtained about potential resolutions of the conflict under study and about how decision makers’ interactions may direct the conflict to distinct resolutions. Analyses also show how political considerations may affect a particular decision maker’s choice, thereby influencing the evolution of the conflict

Status quo analysis of the Flathead River conflict. Water Resources Research

Status quo analysis algorithms developed within the paradigm of the graph model for conflict resolution are applied to an international river basin conflict involving the United States and Canada to assess the likeliness of various compromise resolutions. The conflict arose because the state of Montana feared that further expansion of the Sage Creek Coal Company facilities in Canada would pollute the Flathead River, which flows from British Columbia to Montana. Significant insights not generally available from a static stability analysis are obtained about potential resolutions of the conflict under study and about how decision makers’ interactions may direct the conflict to distinct resolutions. Analyses also show how political considerations may affect a particular decision maker’s choice, thereby influencing the evolution of the conflict

State-of-the-Art Report on Systems Analysis Methods for Resolution of Conflicts in Water Resources Management

Water is an important factor in conflicts among stakeholders at the local, regional, and even international level. Water conflicts have taken many forms, but they almost always arise from the fact that the freshwater resources of the world are not partitioned to match the political borders, nor are they evenly distributed in space and time. Two or more countries share the watersheds of 261 major rivers and nearly half of the land area of the wo rld is in international river basins. Water has been used as a military and political goal. Water has been a weapon of war. Water systems have been targets during the war. A role of systems approach has been investigated in this report as an approach for resolution of conflicts over water. A review of systems approach provides some basic knowledge of tools and techniques as they apply to water management and conflict resolution. Report provides a classification and description of water conflicts by addressing issues of scale, integrated water management and the role of stakeholders. Four large-scale examples are selected to illustrate the application of systems approach to water conflicts: (a) hydropower development in Canada; (b) multipurpose use of Danube river in Europe; (c) international water conflict between USA and Canada; and (d) Aral See in Asia. Water conflict resolution process involves various sources of uncertainty. One section of the report provides some examples of systems tools that can be used to address objective and subjective uncertainties with special emphasis on the utility of the fuzzy set theory. Systems analysis is known to be driven by the development of computer technology. Last section of the report provides one view of the future and systems tools that will be used for water resources management. Role of the virtual databases, computer and communication networks is investigated in the context of water conflicts and their resolution.https://ir.lib.uwo.ca/wrrr/1005/thumbnail.jp