Grouping functions, as one kind of binary continuous aggregation functions, have attracted the continuous attention of scholars since they were proposed. Meanwhile, since Lucca, Sanz and Dimuro et al. proposed the notion of pre-aggregation functions lately, the study on such new “aggregation-like” functions has become a hot topic in the research fields of information fusion. This paper continues to consider the r → -quasi-grouping functions proposed by the author recently based on the grouping functions. At first, we show the relationship among certain classes of r → -quasi-grouping functions. Second, we give the constructions and equivalent characterizations of r → -quasi-grouping functions along with their generalized forms, respectively. Finally, we propose a r → -quasi-grouping functions-based classifier ensemble algorithm ( G -CEA), test the performance of G -CEA through numerical experiments, and verify the effectiveness and stability of G -CEA from comparative analysis with three classical machine learning ensemble algorithms and sensitivity analysis of parameter r → .