A unified model between the weighted average and the induced OWA operator

We present a new model that uses the weighted average (WA) and the induced ordered weighted averaging (IOWA) operator in the same formulation. We call it the induced ordered weighted averaging–weighted average (IOWAWA) operator. We study some of its main properties and we see that it has a lot of particular cases such as the WA and the OWA operator. The main advantage of the IOWAWA operator is that it unifies the IOWA operator with the WA in the same formulation considering the degree of importance that each concept has in the aggregation. We analyze the applicability of this new approach and we see that it is very broad because it can be applied in a wide range of fields such as statistics, economics, decision theory and engineering. Theoretically, we could state that all the previous models and applications based on the WA and the IOWA can be revised and improved with this new approach because they will be included in this framework as a particular case. We focus on an application in a multi-person decision-making in political management.