Multiple criteria group decision making method based on extended hesitant fuzzy sets with unknown weight information

Abstract

In this paper, we initially re-define the existing definition of extended hesitant fuzzy set (EHFS) using the Cartesian product of hesitant fuzzy sets (HFSs). This is while, the EHFS concept should be defined in accordance with the number of decision makers’, and not the number of HFSs. Then we show the superiority of the proposed EHFS to the existing HFS concept by taking multiple criteria group decision making (MCGDM) problems into account in which two nonlinear optimization models are used to evaluate the weights of the decision makers and the weights of the criteria, respectively. As will be discussed in more details, the first optimization model minimizes the divergence degree of individual form of extended hesitant fuzzy decision (IEHFD) matrices, is carried out in Step 2 of the proposed algorithm for solving the MCGDM problem and the second one minimizes the divergence degree between each IEHFD matrix and the collective form of extended hesitant fuzzy decision (CEHFD) matrix, is carried out in Step 3 of the proposed algorithm for solving the MCGDM problem. Finally, we will illustrate the applicability of the proposed method to the other existing ones by dealing with a MCGDM problem under both the hesitant and the extended hesitant fuzzy environments. In addition to that, we will show that the proposed procedure leads to the more desirable result of deciding in comparison with the other existing methods, especially when we are going to generate the criteria weights.