The ordered weighted averaging (OWA) operator of Yager was introduced to provide a method for nonlinearly aggregating a set of input arguments ai. A fundamental aspect of the OWA operator is a reordering step in which the input arguments are rearranged according to their values. Recently, an induced OWA operator was described in which each input argument ai has a single priority αi value. The input arguments are then rearranged according to the priorities αi and not their own values. In this paper we show how the induced OWA operator may be defined when each argument ai has associated with it N priority values αip, p∈{1, 2,…,N}, instead of a single priority value. Finally, we suggest two applications using a multiple priority induced OWA operator. © 2000 John Wiley & Sons, Inc.