On the basis of cluster size and cluster cohesion, we propose a generalized cluster-reliability (CR) measure, which indicates the overall reliability of arguments in a cluster. Taking the reliability of clusters as order-inducing variables, we introduce a generalized cluster-reliability-induced ordered weighted averaging (CRI-OWA) operator from the viewpoint of combining representative arguments of clusters. Furthermore, we propose a grid-based cohesion measure for grid-based clusters. On the basis of this cohesion measure, we obtain the special CR measure and CRI-OWA operator for the grid-based clusters. Then we introduced two other special CR measures for graph-based and prototype-based clusters, respectively. Taking the CR, computed by these two measures, as order-inducing variables, we can obtain two other kinds of CRI-OWA operators for graph-based and prototype-based clusters, respectively. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.