A parametric model for determining consensus priority vectors from fuzzy comparison matrices

We consider a group decision-making problem where a set of alternatives have to be ranked according to fuzzy preference judgments given by multiple experts. We assume that expert assessments are expressed in the form of fuzzy multiplicative preference relations or fuzzy comparison matrices. In this paper we propose a general model to generate crisp priority weights of the alternatives from possibly inconsistent and conflicting fuzzy preference relations. We express our model in terms of matrix approximations to address the consistency problem and we use weighted metrics to simulate the group dynamics. Matrix approximation techniques for deriving a common crisp consistent matrix are extended to work with fuzzy matrices by using the concept of α-cuts. In the aggregation process, the importance of each expert is taken into consideration according to the agreement of the group with the expert. This results in a parametric optimization problem for which a computational formulation is given.