On algebraic properties and linearity of OWA operators for fuzzy sets

Abstract

We deal with ordered weighted averaging operator (OWA operator) on the set of all  fuzzy sets. Our starting point is OWA operator on any lattice introduced in \cite{lizmor2013,ochlizpatbuspal2015}. We focus on a particular case of lattice, namely that of all normal convex fuzzy sets in [0,1], and study algebraic properties and linearity of the proposed OWA operator. It is shown that the operator is an extension of standard OWA operator for real numbers and it possesses similar algebraic properties as standard one, however, it is neither homogeneous nor shift-invariant, i.e., it is not linear in contrast to the standard OWA operator.