Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decision-making method based on the weights of alternatives

A fuzzy cross entropy of the interval-valued intuitionistic fuzzy sets (IVIFSs) (so-called IVIFS cross entropy) is proposed by analogy with the intuitionistic fuzzy cross entropy. In its application to decision-making problems, its optimal decision-making method based on the weights of alternatives is established in which criterion values for alternatives are IVIFSs and the criterion weights are known information. We utilize the interval-valued intuitionistic fuzzy weighted aggregation operators to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then with the ideal and anti-ideal information measures of IVIFS cross entropy, an objective function is constructed to derive the optimal evaluation for the weight of each alternative. The ranking of alternatives and the best one can be determined directly on the basis of the weights of alternatives. Finally, two illustrative examples demonstrate the efficiency of the proposed decision-making method. (C) 2010 Elsevier Ltd. All rights reserved.