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Multi-groups decision making (MGDM) problems, which contain multiple groups of experts acting collectively to evaluate a set of alternatives with respect to several criteria, are focused on in this study. The existing solutions for MGDM are to aggregate the evaluations three times at different levels, which leads to less accuracy and more computational complexities. Intuitionistic-valued hesitant fuzzy elements (I-HFEs) which consider all possible values instead of aggregation straightforward are flexible to represent the experts’ opinions and lessen the steps of aggregations. This study investigates MGDM with decision information taking the form of I-HFEs and their special cases. Based on some aggregation operators of I-HFEs, three approaches for distinct scenarios of MGDM are proposed and clarified by a practical problem involved with supplier selection. Comparisons between the proposed approaches and the existing methods show that the proposed approaches are more rational than those by aggregating the evaluations directly in MGDM.