Variable weights theory and its application to multi-attribute group decision making with intuitionistic fuzzy numbers on determining decision maker's weights.

The determination of the weights of decision makers (DMs) is an important problem in multi-attribute group decision making. Many approaches have been presented to determine DMs' weights. However, the computed weight vectors of DMs are usually assumed to be constant in existing studies, and this may cause irrationalities in the decision results. Therefore, this article proposes a novel method to determine DMs' weights based on variable weights theory in which the evaluation information is described as intuitionistic fuzzy sets (IFSs). First, DMs provide their assessment with IFSs, and the intuitionistic fuzzy weighted averaging (IFWA) operator is applied to obtain weighted decision matrix based on the prior given DMs' and attributes' weights. Second, the DMs' weights are obtained based on variable weights theory, and an alternative decision can be computed. Finally, the converted value of the achieved IFS of each alternative is calculated, and the best appropriate alternative is acquired. Two illustrative examples and the comparisons with exsiting approaches are also used to reflect the effectiveness of the proposed approach.