Induced aggregation operators in the ordered weighted average sum

The ordered weighted average (OWA) aggregation is an extension of the classical weighted average by using a reordering process of the arguments in a decreasing or increasing way. This article presents new averaging aggregation operators by using sums and order inducing variables. This approach produces the induced ordered weighted average sum (IOWAS). The IOWAS operator aggregates a set of sums using a complex reordering process based on order-inducing variables. This approach includes a different types of aggregation structures including the well-known OWA families. The work presents additional generalizations by using generalized and quasi-arithmetic means. The paper ends with a simple numerical example that shows how to aggregate with this new approach.