Involvement of small and medium-scale enterprises is important for developing countries like India. Henceforth, enhancing their competency with the adoption of a suitable enterprise resource planning system (ERPS) is a vital way to enhance their competitiveness. The choice of an appropriate ERPS can be considered as a complex multicriteria decision-making (MCDM) problem where several alternatives (ERPS packages) are assessed based on certain types of characteristics, namely domain knowledge of the supplier, system reliability, service and support, functionality, compatibility, information security, cross-module integration, etc. One critical issue associated with the evaluation of ERPSs is the handling of uncertain information. In this article, we first develop a new methodology to resolve the issue of MCDM problems. In this methodology, the weights of decision experts are systematically calculated with the extended variance approach on intuitionistic fuzzy sets. For calculating the criteria weights, an optimization model based on cross-entropy is proposed, and for the aggregation of the criteria values, a new model called intuitionistic fuzzy improved measurement alternatives and ranking based on the compromise solution is developed, which allows both the vector and linear normalizations and having the advantages of comprising two kinds of aggregation models. Next, an ERPS cloud vendor assessment problem is deliberated with three alternatives (A1: Systems, Applications, and Products (SAP), A2: Oracle Corporation, A3: Microsoft Corporation) and 16 criteria to interpret the reasonableness of the introduced framework. According to the outcomes, SAP is the most suitable alternative. Next, a sensitivity analysis is exhibited with diverse parameter values to inspect the permanence of the presented approach. The advantage of the presented approach is discussed with the comparative investigation.