Recent studies have identified that multi-criteria group analysis methods should take the concepts of risk and uncertainty into account. In some real-life situations, determining the exact values for the potential alternatives' performances and criteria weights is so difficult. To overcome with these situations, their values should be regarded as fuzzy and fuzzy intervals. In this respect, interval-valued hesitant fuzzy sets (IVHFSs) as a suitable modern fuzzy sets theory can be considered because this theory allows decision makers (DMs) to assign some interval-values membership degrees for an alternative in terms of selected criteria under a set to margin of errors. Hence, this paper proposes a novel soft computing approach, namely IVHF-MCGA, based on new interval-valued hesitant fuzzy complex proportional assessment (IVHF-COPRAS) method that can be applied in solving the multi-criteria group decision-making (MCGDM) problems under uncertainty. In this approach, preference values of potential alternatives versus the selected criteria and weights of each criterion are expressed by linguistic variables and then are transformed to interval-valued hesitant fuzzy elements (IVHFEs). In addition, an interval-valued hesitant fuzzy entropy (IVHF-entropy) method is extended to determine the criteria weights by considering the DMs' opinions about the relative importance. Also, a new interval-valued hesitant fuzzy compromise solution (IVHF-CS) method is introduced to estimate the weight of each DM in the group decision-making process along with the last aggregation for the DMs' judgments to avoid the data loss. Then, three practical applications about the robot selection, industrial site selection and rapid prototyping process selection problems are considered to explain steps of the proposed IVHF-MCGA approach and to indicate its validity and applicability. Finally, a comparative analysis between the proposed approach and fuzzy group TOPSIS method is presented based on four comparison parameters, including adequacy to changes of alternatives and criteria, agility in decision process, influence of DMs' weights and impact of first and last aggregations, to show its suitability.