OWA operators defined on complete lattices

Abstract

In this paper the concept of an ordered weighted average (OWA) operator is extended to any complete lattice endowed with a t-norm and a t-conorm. In the case of a complete distributive lattice it is shown to agree with a particular case of the discrete Sugeno integral. As an application, we show several ways of aggregating closed intervals by using OWA operators. In a complementary way, the notion of generalized Atanassov's operators is weakened in order to be extended to intervals contained in any lattice. This new approach allows us to build a kind of binary aggregation functions for complete lattices, including OWA operators.