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This study presents an interval-valued intuitionistic fuzzy cross-entropy measure based on the weighted reduction intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets with adjustable weight vectors as an extension of existing fuzzy cross-entropy measures. Then a decision-making method is developed based on the proposed cross-entropy measure with the optimal weight vectors. In decision making, we establish an optimal model based on the maximum standard deviation of the measure values of the alternatives to search for the optimal weight vectors in the adjustable weight vectors. According to the optimal weight vectors, we can obtain the interval-valued intuitionistic fuzzy cross entropy between the ideal alternative and an alternative to rank the alternatives and to determine the best one. Finally, two illustrative examples are employed to show the feasibility of the proposed method in practical applications, and then the comparison of the proposed method with existing relevant methods is given to demonstrate that the proposed method is the further improvement and generalization of the existing relative methods.

Decision-Making Method Using Interval-Valued Intuitionistic Fuzzy Cross-Entropy Based on the Weighted Reduction Intuitionistic Fuzzy Sets