On distributivity and conditional distributivity of S-uninorms over uninorms

Abstract

Aggregation operators with an annihilator are in the focus of a significant number of research papers due to their applicability in both theoretical and practical areas of mathematics. Therefore, the main topic of this paper is distributivity and conditional distributivity for some classes of aggregation operators with this property. The characterization of all pairs (F,G) of aggregation operators that are satisfying distributivity law, on both whole and restricted domain, where F is a S-uninorm from Umin, and G is a t-norm or a uninorm from Umin or Umax is given.