Conflict analysis based on three-way decision for triangular fuzzy information systems

Triangular fuzzy numbers (TFNs) can not only provide the range of fuzzy points, but contain the three most representative fuzzy points, which play an essential role in describing fuzzy information. Combining with conflict situations, the agents' caution in the decision-making process can be well depicted by TFNs. However, little effort has been paid to conflict analysis on triangular fuzzy information systems (TFISs). In this paper, we study three-way conflict analysis based on TFISs. First, we propose the concept of TFISs and then establish a TFIS for conflict analysis. Further, relative area ΔS is defined to describe concrete attitudes of agents about issues. Second, since the importance of the same issue may vary for agents, we attach fuzzy weights to issues according to triangular fuzzy symmetric judgment matrices (TFSJMs) of agents. Third, we determine the total attitude of each agent to all issues. Then we illustrate how to compute thresholds α and β using the theory of triangular fuzzy decision-theoretic rough sets. Finally, a tri-partition of agents is obtained based on the thresholds.