Vector induced OWA operators

Information aggregation often requires ordering of data based on different criteria, leading to the introduction of functions like Ordered Weighted Averaging (OWA) and Induced Ordered Weighted Averaging (IOWA) operators. The sorting of vector information is not trivial, and so far no induced aggregation operators have been studied in the multivalued context. We introduce the Vector Induced Ordered Weighted Averaging (VIOWA) operators, a vector extension of IOWA designed for aggregating multivalued data. We define VIOWA operators based on admissible orders, using all admissible permutations, and we explore its formulation using the best admissible permutations based on the degree of totalness. Additionally, we analyze the basic properties of these methods and their interrelations. To demonstrate the effectiveness of VIOWA operators, we apply them to multivalued time series prediction, in order to aggregate several vector-valued model predictions. Experiments on five datasets show the usefulness of VIOWA operator-based aggregation, outperforming individual models and other classical aggregation methods, highlighting its potential in multivariate settings.