Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets

A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under interval-valued intuitionistic fuzzy environment for the some situations where the information about criteria weights for alternatives is completely unknown. To determine the entropy weights with respect to a decision matrix provided as interval-valued intuitionistic fuzzy sets (IVIFSs), we propose two entropy measures for IVIFSs and establish an entropy weight model, which can be used to determine the criteria weights on alternatives, and then propose an evaluation formula of weighted correlation coefficient between an alternative and the ideal alternative. The alternatives can be ranked and the most desirable one(s) can be selected according to the values of the weighted correlation coefficients. Finally, two applied examples demonstrate the applicability and benefit of the proposed method: it is capable for handling the multicriteria fuzzy decision-making problems with completely unknown weights for criteria.