Quality function deployment (QFD) is a customer-oriented tool for developing products. Based on the idea of the best-worst method (BWM), a novel model is developed to determine the relative importance ratings (RIRs) of customer requirements (CRs) with interval grey linguistic (IGL) information, which plays a significant role in QFD. CRs are rated with IGL variables, and the degree of greyness degree function that can be used to handle the IGL variables is defined based on the power utility function. Then, considering customer heterogeneity, a model is constructed to derive the RIRs of CRs by following the logic of the BWM. Finally, a case study of 5 G smartphone development is provided to verify the validity and the feasibility of the proposed method.