Due to the budgetary deadlines and time to market constraints, it is essential to prioritize software requirements. The outcome of requirements prioritization is an ordering of requirements which need to be considered first during the software development process. To achieve a high quality software system, non-functional requirements (NFRs) must be taken into consideration throughout the prioritization process. Although several requirements prioritization methods have been proposed so far, the research on prioritizing non-functional requirements is limited. In this paper, we propose a quantitative approach based on Fuzzy Logic and Alpha cut approach which aims to perform the process of prioritizing non-functional requirements. Application of the proposed approach provides the practitioners with a prioritized list of non-functional requirements which are prioritized based on their relationship with functional requirements (FRs).