<p>This study analyzes the challenges of collaborative innovation systems (CISs) that may arise in public higher education institutions (PHEIs) in the time of Industry 4.0 (I4.0). A hybrid decision-making framework is further developed under the background of interval-valued intuitionistic fuzzy sets (IVIFSs). First, a systematic literature analysis is conducted to assess the key challenges of CISs in PHEIs in the I4.0 era. Second, a novel distance measure (DM) is presented to compute the discrepancy degree on IVIFSs. Third, a novel weight-determining tool is developed by combining the objective weight of challenges using the proposed DM-based approach and the subjective weight of challenges with the help of interval-valued intuitionistic fuzzy-RANking COMparison (IVIF-RANCOM) model. Fourth, with the integration of Einstein triangular norms and power operations, some Einstein power-weighted aggregation operators (AOs) are introduced to aggregate the interval-valued intuitionistic fuzzy numbers (IVIFNs). Based on the criteria weighting tool and Einstein power-weighted AOs, a modified combined compromise solution (CoCoSo) approach is d to recognize and evaluate the main challenges of CIS in PHEIs under the context of IVIFSs. Finally, a case study of an Indian state is investigated along with sensitivity and comparative analyses to validate the efficiency and applicability of the model. The research concludes that lack of e-learning tools and resources (0.1903) is the most important challenge for evaluating the challenges of CIS in PHEIs in the I4.0. Competence of the teachers (0.1885) is the second most effective challenge for evaluating the challenges of CIS in PHEIs in the I4.0. In addition, option PHEI-1 (0.875) is the optimal choice among the other institutions to evaluate the challenges of CIS in PHEIs in the I4.0.</p>