We present the uncertain induced quasi-arithmetic OWA (Quasi-UIOWA) operator. It is an extension of the OWA operator that uses the main characteristics of the induced OWA (IOWA), the quasi-arithmetic OWA (Quasi-OWA) and the uncertain OWA (UOWA) operator. Thus, this generalization uses quasi-arithmetic means, order inducing variables in the reordering process and uncertain information represented by interval numbers. A key feature of the Quasi-UIOWA operator is that it generalizes a wide range of aggregation operators such as the uncertain quasi-arithmetic mean, the uncertain weighted quasi-arithmetic mean, the UOWA, the uncertain weighted generalized mean, the uncertain induced generalized OWA (UIGOWA), the Quasi-UOWA, the uncertain IOWA, the uncertain induced ordered weighted geometric (UIOWG), and the uncertain induced ordered weighted quadratic averaging (UIOWQA) operator. We study some of the main properties of this approach including how to obtain a wide range of particular cases. We further generalize the Quasi-UIOWA operator by using discrete Choquet integrals. We end the article with an application of the new approach in a decision making problem about investment selection. © 2010 Wiley Periodicals, Inc.