Some properties and representation methods for Ordered Weighted Averaging operators

This study demonstrates or proposes some new properties and representation methods for Ordered Weighted Averaging (OWA) operators. The interweaving representation allows some well-known OWA operators to be decomposed into two other well-known OWA operators. A theorem is proposed for determining the relations between OWA operators with respect to their degree of orness/andness. We also provide a complex iteration method for well-known OWA operators, as well as some new generation methods and possible adjustment methods for well-known Centered OWA operators. Furthermore, we investigate some new methods for generating Step OWA and orlike/andlike window OWA operators, where these methods are accurate in terms of their orness/andness degree. We also demonstrate two interesting and useful properties of OWA operators, i.e., Stage OWA and Dew OWA, and one of their applications.