Family of Maximal Consistent Alliance Interval Sets in Incomplete Heterogeneous Conflict Information System

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.

Keywords

• three-way decision; conflict analysis; incomplete heterogeneous information system; maximal clique; family of maximal consistent alliance interval sets