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

Three-way decision is a decision-making model in line with people's cognition and aims to think and deal with problems at three levels or three aspects. One of the main purposes of conflict analysis is to partition the set of agents into three coalitions called positive alliance, central alliance and negative alliance in order to determine the relationship between two agents. Recently, researchers combine these two closely related directions to form a new research topic: three-way conflict analysis. This paper consider the case that the attitude of an agent on an issue is a trapezoidal fuzzy number. Firstly, we provide a trapezoidal fuzzy information system for conflict analysis and then we transform attitudes of agents from trapezoidal fuzzy numbers to real numbers through the expectation of trapezoidal fuzzy numbers. Secondly, conflict analysis for a single issue is investigated and three alliances based on a pair of thresholds are obtained. As for multiple issues, it is necessary to integrate multiple attitudes for a collection of issues to one. Considering different importance of issues, we develop a new method to integrate attitudes based on the variance of trapezoidal fuzzy numbers, and then we come up with a conflict analysis model for multiple issues. Thirdly, a method to calculate thresholds is proposed based on decision-theoretic rough sets so as to acquire three alliances based on a single issue or multiple issues more reasonably. Finally, we devote to ranking all the issues according to the conflict degree among agents and our method may be instructive to promote the resolution of conflict situations.