Three-way conflict analysis and resolution based on interval set information

Abstract

In existing three-way conflict analysis (TWCA), once the ratings are given, the relationships between agents will be determined. However, agents may compromise to achieve a common goal when conflicts arise, which leads to variable ratings. This paper will present a novel TWCA model based on interval sets, where the ratings are represented by interval sets (the lower bound of an interval set represents the preferred rating, and the upper bound indicates the range of acceptable ratings). First, we give the notion of interval set conflict systems (ISCSs) and introduce a new conflict function. Second, considering the balance of agents' opinions, we assign issue weights according to the proportion of the absolute values of the column means of all agents' ratings (ACMR) across different issues. We then discuss the trisections of agent pairs, agent set, and issue set, where the thresholds are derived by the given conflict function. We propose two methods for conflict resolution by adjusting the preference ratings of some agents to form a maximal alliance among as many agents as possible. We verify the model's stability and validity through sensitivity analysis and comparative analysis. Finally, we apply this model to a case study of enterprise bidding.