Enterprise Resource Planning (ERP) software selection is one of the most important decision making issues covering both qualitative and quantitative factors for organizations. Multiple criteria decision making (MCDM) has been found to be a useful approach to analyze these conflicting factors. Qualitative criteria are often accompanied by ambiguities and vagueness. This makes fuzzy logic a more natural approach to this kind of problems. This study presents a beneficial structure to the managers for use in ERP software vendor selection process. In order to evaluate ERP vendors methodologically, a hierarchical framework is also proposed. As a MCDM tool, we used analytic hierarchy process (AHP) and its fuzzy extension to obtain more decisive judgments by prioritizing criteria and assigning weights to the alternatives. The objective of this paper is to select the most appropriate alternative that meets the customer's requirements with respect to cost and quality constraints. In the end of this study, a real-world case study from Turkey is also presented to illustrate efficiency of the methodology and its applicability in practice.