Mixed Solution Strategy for MCGDM Problems Using Entropy/Cross Entropy in Interval-Valued Intuitionistic Fuzzy Environment

Although several weight determining methods have been studied for multiple criteria group decision making (MCGDM) problems under intuitionistic fuzzy environment, in the present study, besides the criteria values provided by the decision makers (DMs), we propose to also use the historical data of alternatives-criteria to compute the criteria weights. This is a reasonable thought as the past information may influence the decision makers' choice of entries in their respective alternatives-criteria decision matrices. To this aim, we introduce a novel mixed solution strategy to derive the criteria final weight vector. Initially, the alternatives-criteria decision matrices provided by the DMs are taken to involve interval-valued intuitionistic fuzzy numbers (IVIFNs). The entropy measure for IVIFNs, studied by Ye [2010a], is used to aggregate these decision matrices. We also introduce a new definition of cross entropy for IVIFNs and used it to rank the alternatives. Finally, an example is presented to illustrate the proposed approach.