Multiattribute group decision making based on interval-valued intuitionistic fuzzy sets and analytically evidential reasoning methodology

The existing multiattribute group decision making methods with interval-valued intuitionistic fuzzy (IVIF) sets only consider weights of the experts who participated in decision making, however the reliabilities of that are not considered at all. In order to solve this problem and make a much scientific decision, a transformation method from IVIF value to belief degree is defined based on the frame of discernment consisting of only excellent and non-excellent two hypotheses. Then the basic probability assignment (BPA) function computing method is introduced by discounting belief degrees with both weights and reliabilities. The derived BPA functions are combined by the analytically evidential reasoning (ER) methodology for two times, the one is to combine BPA functions on all attributes with respect to a specified expert, and the other is to combine the combined BPA functions for all experts with respect to a specified alternative. Finally, the relative coefficient is employed to rank the alternatives with IVIF sets. An example is proposed to illustrate the decision making process by the proposed method.