Digital technology advancement and the Internet of Things (IoT) are playing a major role to take a big leap towards achieving Industry 4.0. Cloud-based data management and big data analytics have given rise to adopt Cloud Enterprise Resource Planning (CERP). The CERP has become a significant tool for the success of the information management system (IMS) which is ultimately responsible for the success of any organization. The selection of CERP depends on many critical success factors (CSFs) that must be considered while evaluating and selecting a CERP. In this work, identified CSFs of CERP are modeled using a multi-criteria decision-making (MCDM) approach. The Analytic Hierarchy Process (AHP) and Fuzzy Analytic Hierarchy Process (FAHP) based modelling have been carried out to derive the ranking of the CSFs responsible for the CERP. The group decision-making (GDM) based AHP has also been adopted to build the decision-making model. The paper models 5 Dimensions and 20 sub-criteria factors to provide the prioritized rank of Dimensions and CSFs. The AHP and FAHP models identify the ranking of the 5 Dimensions as Organizational Behavior, Cloud ERP Essentials, Technological Advancement, Innovational Ideas, and Environmental Impact.