In this paper, we propose new aggregation operators for multi-criteria decision making under linguistic settings. The proposed operators are based on two sets of criteria weights. Besides the primary conventional criteria weights, we introduce a method to deduce secondary criteria weights from the criteria evaluations, which reflect the role of the different criteria in discriminating among the alternatives. The properties of the proposed operators are investigated. An approach for the application of the said operators in a group multi-criteria decision making problem is presented. Following the same, the proposed operators are applied in a case study on supplier selection. The empirical validation of the proposed operators is performed on a set of 12 real datasets.