We present a new approach that unifies the induced generalized ordered weighted averaging (IGOWA) operator with the weighted average (WA) when the available information is uncertain and can be assessed with interval numbers. We call it the uncertain induced generalized ordered weighted averaging – weighted averaging (UIGOWAWA) operator. The main advantage of this approach is that it unifies the IOWA and the WA taking into account the degree of importance of each case in the formulation and considering that the information is given with interval numbers. We also study different properties of the UIGOWAWA operator and different particular cases. We also analyze the applicability of the new approach and we see that it is possible to develop a wide range of applications because all the previous studies that use the WA can be revised and extended with this new approach. We focus on an application in decision making with the theory of expertons. Thus, we are able to assess group decision making problems in a more complete way.
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