A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices

This paper presents a model for a group decision-making problem with interval preference matrices. First, a new definition of interval additive reciprocal matrices with multiplicative consistency is given. Transformation methods between interval additive and multiplicative reciprocal matrices are proposed and applied to homogenize interval preference matrices. Second, the consistency of interval multiplicative reciprocal matrices is utilized to propose a generalized ordered weighted geometric averaging operator, which permits the aggregation of interval multiplicative reciprocal matrices in such a way that more important weight is given to that with more consistency. In order to avoid a misleading solution, the consistency and acceptable consistency of the collective interval multiplicative reciprocal matrix are studied in detail. Finally, a new algorithm is presented to solve the group decision-making problem with interval preference matrices. Numerical results are carried out to illustrate the given definitions, methods and algorithm, respectively.