Matrix representation and extension of coalition analysis in group decision support

Coalition stability is extended to include uncertain preference using matrix representation within the framework of the graph model for conflict resolution. Coalition stability analysis within a graph model provides guidance for decision makers and analysts by providing an assessment of whether states that are individually stable are unstable for coalitions. In using the graph model method for conflict resolution one carries out stability analysis of a graph model, and then follows up with post-stability analysis, an important component of which is coalition analysis. Although basic coalition stabilities have been defined for the graph model, they are based on a transitive graph, which is inconsistent with the standard restriction in the graph model. Algorithms for implementing these coalition stabilities have not been developed, because the nature of their logical representations makes coding difficult. Additionally, existing coalition stabilities apply only to simple preference, which limits their utility for exploring more complicated applications in practice. In this paper, coalition stabilities are extended to include uncertain preference and represented using matrices, which are more effective and convenient for computer implementation and for adaptation to new analysis techniques.