The Ordered Weighted Average in the Variance and the Covariance

The ordered weighted average (OWA) is an aggregation operator that provides a parameterized family of aggregation operators between the minimum and the maximum. This paper analyzes the use of the OWA in the variance and the covariance. It presents several extensions by using a unified framework between the weighted average and the OWA. Furthermore, it also develops other generalizations with induced aggregation operators and by using quasi-arithmetic means. Several measures of correlation by using the OWA are introduced including a new type of Pearson coefficient. The paper ends with some numerical examples focused on the construction of interval and fuzzy numbers with the variance and the covariance.