Discrete and continuous recursive forms of OWA operators

Abstract

We firstly present an evaluation problem for online shop based on gradually increasing number of inputs. Then we propose a model using Recursive OWA operator with constant orness/andness grade involved. Next, we analyze properties of discrete Recursive OWA operators, show their relationship with Pascal Triangle and further generalize this relationship to Γ function. For the continuous case, we propose a concept of self-similar ordered weighting functions (OWF) and analyze some properties of OWF. Using these concepts, we present the recursive aggregation method of continuous arguments under continuous OWF. We show a relationship of OWF with the Regular Increasing (RIM) quantifier. Furthermore, based on an isomorphism relation between discrete and continuous recursive OWA operators, Left Recursive OWA can be seen as the discrete form of continuous OWF.