A multi-criteria fuzzy decision-making method based on weighted interval-valued intuitionistic fuzzy number correlation coefficients is proposed for some situations where the information about criteria weights for alternatives is completely unknown．It hopes to supplement the insufficiency of the method based on distance measure of IVIFSs．Meanwhile this method reduces the loss of evaluation information by taking into account the influence of hesitancy degree．A non-linear programming model is established based on the maximization of the correlation coefficient between each alternative and the ideal ( critical) alternative．The model can be used to get the criteria weights from a new perspective．Then，we proposed a relative closeness of the weighted correlation coefficients between an alternative and the ideal alternative in order to rank the alternatives．Finally，a comparative analysis demonstrates the effectiveness of the proposed method．