Fuzzy option prioritization for the graph model for conflict resolution

A fuzzy option prioritization technique is developed to efficiently model uncertain preferences of DMs in strategic conflicts as fuzzy preferences by using the decision makers' (DMs') fuzzy truth values of preference statements at feasible states within the framework of the Graph Model for Conflict Resolution. 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. A fuzzy preference formula is introduced based on the fuzzy truth values of preference statements, and it is established that the output of this formula is a fuzzy preference relation. It is shown that fuzzy option prioritization can also be used when the truth values of preference statements at feasible states are completely based on Boolean logic, thereby generating a crisp preference over feasible states that is the same as would be found by employing the existing crisp option prioritization, making the crisp option prioritization technique a special case of the fuzzy option prioritization methodology. To demonstrate how this methodology can be employed to represent fuzzy preferences in real-world decision problems, fuzzy option prioritization is applied to an actual dispute over groundwater contamination that took place in Elmira, Ontario, Canada.