The grouping weighted averaging operator via three-way conflict analysis

Abstract

Aggregation operators play an important role in problems related to information fusion. There are various aggregation operators, and selecting appropriate ones for a specific problem remains a challenging task. For the evaluation problem in three-way conflict analysis, this paper attempts to propose a new type of aggregation operator: the grouping weighted averaging (GWA) operator. GWA operators not only consider the implicit information in data, but also do not require strong prior knowledge of data to be aggregated. First, we divide the data into groups, which correspond to coalitions in three-way conflict analysis. Second, weights of groups are generated according to their properties. Third, the final result is obtained via two aggregations: within and between groups. Besides, we also provide multiple GWA operators based on various partitions and weight allocation methods, and study their theoretical properties. Especially, as an application to conflict analysis, we propose an index of stability based on the GWA operator to compare coalition systems.