Nonlinear Optimization Models for Multi-Attribute Group Decision Making with Intuitionistic Fuzzy Information

Xu and Cai (2010) investigate multi-attribute group decision making problems in which the attribute values provided by experts are expressed in IFNs. Each of the attributes is composed of a membership degree, a non-membership degree, and an indeterminancy degree, and the weight information about both the experts and the attributes is to be determined. They first unify different types of attribute values so as to facilitate inter-attribute comparisons, and employ the simple additive weighting method to fuse all the individual opinions into the group one. They then develop two nonlinear optimization models, one minimizing the divergence between each individual opinion and the group one, and the other minimizing the divergence among the individual opinions, from which two exact formulas can be obtained to derive the weights of experts. To maximize group consensus, they establish a nonlinear optimization model based on all the individual intuitionistic fuzzy decision matrices to determine the weights of attributes. The simple additive weighting method is used to aggregate all the intuitionistic fuzzy attribute values corresponding to each alternative, and then the score function and the accuracy function are employed to rank and select the given alternatives. Moreover, they extend all the above results to interval intuitionistic fuzzy situations, and apply the models developed to an air-condition system selection problem.