M. Abul Bashar

Grey-Based Preference in a Graph Model for Conflict Resolution With Multiple Decision Makers

To capture uncertainty in preferences, definitions based on grey numbers are incorporated into the graph model for conflict resolution (GMCR), a realistic and flexible methodology to model and analyze strategic conflicts. A general grey number is a real number that may be a member of a discrete set of real numbers, or may fall within one or several intervals. It can represent uncertain preference of decision makers in a meaningful way. Here, a grey-based preference structure is developed and integrated with GMCR. Utilizing a number of grey-based ideas, solution concepts describing human behavior under conflict in the face of uncertain preference are defined for a conflict model. This grey-based GMCR is then applied to a generic sustainable development conflict with uncertain preferences in order to demonstrate how it can be conveniently utilized in practice.

Modeling Fuzzy and Interval Fuzzy Preferences Within a Graph Model Framework

A methodology is developed to model a decision makers (DMs) fuzzy and/or interval fuzzy preference over feasible scenarios or states within the framework of the graph model for conflict resolution. This technique uses the DMs fuzzy relative importance of its preference statements and their fuzzy truth values for the feasible states in a conflict under uncertain conditions. A preference statement of a DM is a preferable combination of DMs options or courses of action. The fuzzy importance for one preference statement over another, a value in the interval [0, 1], is interpreted as the degree to which the first preference statement is more important than the second to the DM. A fuzzy truth value of a preference statement at a feasible state is a number in the interval [0, 1] that represents the degree to which the statement is true at the state. When the DM is confident in its pairwise fuzzy importance degrees over the preference statements and their fuzzy truth values at the feasible states, the methodology provides a fuzzy preference over the states. When there is an ordinary or crisp importance ordering of preference statements and when the truth values of preference statements are classical or crisp at the feasible states, the technique generates a crisp preference over the states. The methodology is illustrated using a case study.

Coalition fuzzy stability analysis in the Graph Model for Conflict Resolution

Coalition fuzzy stability concepts are developed within the Fuzzy Preference Framework for the Graph Model for Conflict Resolution to investigate how decision makers can cooperate. The objective is to identify favorable outcome(s) in a multiple participant-multiple objective decision problem with fuzzy preference information. More specifically, coalition versions of fuzzy Nash stability, fuzzy general metarationality, fuzzy symmetric metarationality, and fuzzy sequential stability are proposed. They constitute a natural generalization of the corresponding non-cooperative fuzzy preference-based definitions for Nash stability, general metarationality, symmetric metarationality, and sequential stability, respectively. Coalition fuzzy stability definitions are employed to analyze an actual dispute over groundwater contamination in Elmira, Ontario, Canada, demonstrating how these new concepts can be conveniently applied to practical problems in order to gain valuable strategic insights.

Fuzzy preferences in a two-decision maker graph model

A fuzzy preference framework is developed within the paradigm of the graph model for conflict resolution. This framework takes into account both certain and uncertain information about the preferences of decision makers (DMs) involved in a strategic conflict. The graph model is a solution methodology for conflict decision making that begins with a model of the problem and suggests possible resolutions through a number of stability definitions. Four basic fuzzy stability definitions are introduced for a two-DM graph model to analyze conflict behavior and identify possible resolutions even when preferences are fuzzy. Fuzzy stability definitions describe varied human behavior in a conflict model; a state is fuzzy stable for a DM according to a specific fuzzy stability definition if a move to any other state, evaluated according to that definition, does not meet the DMs fuzzy satisficing threshold. A state that is fuzzy stable for all DMs under a specific fuzzy stability definition constitutes a fuzzy equilibrium under that definition, and is interpreted as a possible resolution of the conflict. Fuzzy stability definitions include fuzzy Nash stability, fuzzy general metarationality, fuzzy symmetric metarationality, and fuzzy sequential stability.

A Basic Hierarchical Graph Model for Conflict Resolution with Application to Water Diversion Conflicts in China

Abstract A basic hierarchical graph model with three decision makers is developed and used to analyze a water diversion conflict in China. This hierarchical graph model combines two component graph models. The theoretical framework of the combined model is constructed using the decision makers, states, moves, and preference structures from the component models. Theorems are developed to relate stable states in the hierarchical model to stable states in local graph models. This novel approach can avoid direct calculation for four hierarchical stabilities. This methodology is applied to a water diversion conflict in China, consisting of conflicts at two locations where it is proposed to divert water from the south to the north of the country. The analytical results show how decision makers can obtain strategic resolutions for the entire conflict.

First-Level Hypergame for Investigating Misperception in Conflicts

A new technique is introduced to model misperception by participating decision makers (DMs) in a conflict having two or more DMs within the framework of the graph model for conflict resolution. This comprehensive approach enables one to model a conflict situation involving misperception: held by and about the focal DM and its opponents. To achieve this, DMs’ options in a conflict situation are classified based on different kinds of misperception that can alter the choices of the focal DM and/or the other DMs. Furthermore, the combination of DMs’ options can generate the universal set of options for the entire conflict, which can then be used to construct the universal set of states. This novel design can differentiate between the states that are recognized by all DMs and those that are recognized individually. Furthermore, eight sets of equilibria are formally defined within the construction of the first-level hypergame in graph form to provide strategic insights into the conflict and reflect the effect of DMs’ misperceptions on the equilibria of the dispute.

A Case Study of Grey-Based Preference in a Graph Model for Conflict Resolution with Two Decision Makers

A generic sustainable development conflict having uncertain preferences is investigated using a new methodology. In particular, definitions of grey numbers are introduced for incorporation into the Graph Model for Conflict Resolution (GMCR) in order to capture uncertainty in preferences. The GMCR constitutes a simple and flexible methodology model and analyze strategic conflicts. The goal of the study is to analyze the influence of uncertainty on the outcome of the conflict and to provide suggestion on guiding the conflict to move in a desired direction. General grey numbers are used to represent the uncertain preferences of decision makers. Following the explanation of four solution concepts based on grey preferences, a stability analysis is conducted and some new insights are provided in this research.

Fuzzy preferences in the sustainable development conflict

A Fuzzy Preference Framework for the Graph Model for Conflict Resolution is employed to analyze the sustainable development conflict in order to gain strategic insights. This framework is a novel methodology to identify outcomes favorable for all parties in a multiple-participant multiple-objective decision making setting with both certain and uncertain preference information. When applied to the sustainable development conflict, in which a developer plans to build or operate a project inspected by an environmental agency, the methodology identifies stable outcomes and thus clarifies the necessary conditions for sustainability.

Fuzzy preferences in conflict resolution

A systematic study of recent developments in preferences based on fuzzy logic is carried out in order to identify an effective design for fuzzy preference models in conflict resolution. Fuzzy preference, defined via a fuzzy relation over the alternatives or states, attempts to represent a decision makers preferences more realistically. It generalizes the usual preference structures in the sense that it provides a uniform description of both certain (crisp) and uncertain preferences. The potential applicability of fuzzy preferences to the modeling, analysis, and understanding of strategic conflicts is investigated and connected to a literature survey.