The objective of this study is to introduce some covariance ordered weighted logarithmic averaging (Cov-OWLA) operators . Covariance measures the conduct of one variable based on the behavior of another; this characteristic makes it key for decision-making processes, especially when applied in uncertain environments. We present some families and particular cases of the introduced operators, including their generalized, induced, and generalized induced formulations. An illustrative example using real-world data on tourism gross domestic product and homeland security indicators is proposed. The results show that there was a positive linear relation between the introduced variables. In this scenario, crime did not affect tourist activity, but tourist activity incited crime. The resulting aggregation with Cov-OWLA operators shows a generally better fit when compared to traditional methods.