New Models of Three-Way Conflict Analysis for Incomplete Situation Tables

For conflict problems, attitudes of agents on issues are often lost due to some mistakes, and trisecting a set of agents is an important research topic of conflict analysis, and three-way decisions with rankings and references provides an effective method for trisecting a set of agents. In this paper, we divide a set of issues into two disjoint parts from different perspectives, and give the support and opposition rankings of issues and the support and opposition reference tuples for an incomplete situation table. Then, we design an alliance measure with regard to an issue by a transition probability function, and develop an additive alliance measure regarding multiple issues with conditional weights of issues. Afterwards, we take the additive alliance measure to trisect a set of agents towards multiple issues, and give three types of decision rules by considering the weights of agents. Finally, we design an algorithm for deriving three types of decision rules, and use an example to show how to make decisions with the proposed model.