The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.

► Core concepts in information sciences, insurance and finance are connected. ► Ordered weighted averaging operators aggregate fuzzy rules into a single value. ► Distortion risk measures summarize the risk of a loss distribution in a single value. ► The relationship between them is shown for discrete and finite random variables. ► The degree of orness indicator characterizing distortion risk measures is introduced.