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The paper presents a novel multiple attribute decision-making (MADM) approach for the problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy sets (IVIFS). First, the fuzzy cross entropy and discrimination degree of IVIFS are defied. Subsequently, based on the discrimination degree of IVIFS, a nonlinear programming model to minimize the total deviation of discrimination degrees between alternatives and the positive ideal solution PIS as well as the negative ideal solution (NIS) is constructed to obtain the attribute weights and, then, the weighted discrimination degree. Finally, all the alternatives are ranked according to the relative closeness coefficients using the extended TOPSIS method, and the most desirable alternative is chosen. The proposed approach extends the research method of MADM based on the IVIF cross entropy. Finally, we illustrate the feasibility and validity of the proposed method by two examples

A Novel MADM Approach Based on Fuzzy Cross Entropy with Interval-Valued Intuitionistic Fuzzy Sets