Probabilistic Option Prioritizing in the Graph Model for Conflict Resolution

Probabilistic preferences have been proposed in the graph model for conflict resolution (GMCR) to accommodate both situations in which a decision maker (DM) vacillates in which criteria to use when comparing two scenarios and also situations in which there is uncertainty regarding who will act as a DM representative. In this paper, we propose two option prioritizing techniques to obtain probabilistic preferences in the GMCR more efficiently. The crisp preference option prioritizing relies on an ordered sequence of preference statements that determines the crisp preference relation. In the first proposed technique, a probability distribution is associated with a class of ordered sequences of preference statements of the DM, where the probability of state s being preferred to state t by the DM consists of the sum of the probabilities of the ordered sequences of preference statements where s is preferred to t according to the crisp preference based on the corresponding ordered sequence of preference statements. In the second technique proposed, we allow for uncertainty both on the set of preference statements considered by a DM and also on which preference statement within the set is the most important one for him. An application is provided to illustrate the use of these techniques.