Abstract: As effective tools for dealing with uncertainty, three-way decision models have been widely applied in the study of conflict analysis. However, existing three-way conflict analysis models are mostly based on single-type conflict information systems, which fail to address the challenges of practical situations where agents may have missing or multiple types of ratings. Furthermore, the existing definitions of alliance sets are typically based on a given agent. Particularly, agents in an alliance set are allied to the given agent, but they are not necessarily allied with each other. To address these issues, this paper proposes a three-way conflict analysis model in an incomplete heterogeneous conflict information system. Additionally, this paper presents the definition and algorithm of a family of maximal consistent alliance interval sets, where agents are allied with each other. Firstly, the incomplete heterogeneous conflict information system with single-dimensional multi-type ratings is transformed into a two-dimensional fuzzy incomplete conflict information system with two-dimensional single-type ratings. This is achieved by defining the support and opposition degrees for different rating types of agents. Secondly, the agent-based alliance, conflict, and neutral interval sets using optimistic and pessimistic distance functions between agents are defined. Finally, a family of maximal consistent alliance interval sets is defined and obtained by adopting the algorithm of maximal clique enumeration.

Key words: three-way decision, conflict analysis, incomplete heterogeneous information system, maximal clique, family of maximal consistent alliance interval sets

摘要： 作为处理不确定性问题的有效工具，三支决策已被广泛应用于冲突分析研究中。然而，现有的三支冲突分析模型大多基于单一类型的冲突信息系统，难以应对实际应用中代理对议题具有多类型评价值和缺失值的情况。同时，已有联盟集的定义通常基于给定代理，即联盟集中的代理与给定代理具有联盟关系，但不一定两两联盟。为了解决这些问题，构建了基于不完备异构冲突信息系统的三支冲突分析模型，并提出了代理两两相关的极大一致联盟区间集族的定义及其构造算法。首先，通过定义代理不同类型评价值的支持度和反对度，将对单个议题单维度多类型评价值的不完备异构冲突信息系统转化为双维度同类型评价值的二维模糊不完备冲突信息系统。其次，通过定义代理之间的乐观与悲观距离函数，构造了基于代理的联盟、冲突、中立区间集。最后，定义了极大一致联盟区间集族，并利用极大团的枚举算法获取极大一致联盟区间集族。

关键词: 三支决策, 冲突分析, 不完备异构信息系统, 极大团, 极大一致联盟区间集族