Three-way Conflict Analysis: Alliance, Conflict, and Neutrality Reducts of Three-valued Situation Tables

In a three-valued situation table, there are different levels of importance for different issues with respect to the alliance, conflict, and neutrality relations, and it is necessary to distinguish all issues as reducible and irreducible elements to filter out the key issues for solving conflicts. However, we have not observed studies of issue reduction for three-valued situation tables in three-way conflict analysis. In this paper, first, we give the matrix representations of alliance, conflict, and neutrality relations and reveal the relationship between two agents in the framework of a matrix. Then, we propose the concepts of alliance, conflict, and neutrality reducts of three-valued situation tables and define reducible and irreducible elements with respect to the alliance, conflict, and neutrality relations. Additionally, we design sequential forward and backward heuristic algorithms for constructing the alliance, conflict, and neutrality reducts. Finally, we give discernibility matrices for computing the sets of all alliance, conflict, and neutrality reducts, and we employ several examples to illustrate how to construct all alliance, conflict, and neutrality reducts. We provide an application of issue reduction to help the government of Gansu Province make a development plan for next year.