A note on distributivity and conditional distributivity for S-uninorms

Abstract Although Fang and Hu systematically discussed distributivity and conditional distributivity for S-uninorms, Fang and Hu mistook the neutral element of the underlying uninorm of the observed S-uninorm (resp. T-uninorm) for the IFC element of the observed S-uninorm (resp. T-uninorm). Thus, a table is provided to summarize all the related wrong conclusions in the work of Fang and Hu instead of correcting them one by one. Moreover, there are some other faults in the characterizations of the distributivity for a uninorm in U min over a T-uninorm with the underlying uninorm in U max , a t-conorm over an S-uninorm with the underlying uninorm in U min , a uninorm in U max over an S-uninorm with the underlying uninorm in U min and so on. This paper intends to remedy these defects. The legible calculation formulae of the IFC elements of S-uninorms with the underlying uninorms in U min and T-uninorms with the underlying uninorms in U max are provided. For readers' convenience, a table is given to show the correspondences among the conclusions.