Norms Induced from OWA Operators

We describe the basic properties of a norm and introduce the Minkowski norm. We then show that the OWA aggregation operator can be used to provide norms. To enable this we require that the OWA weights satisfy the buoyancy property, w(j) >= w(k) for j < k. We consider a number of different classes of OWA norms. It is shown that the functional generation of the weights of an OWA norm requires the weight generating function have a non-positive second derivative. We discuss the use of the generalized OWA operator to provide norms. Finally we describe the use of OWA operators to induce similarity measures.