Distributivity and conditional distributivity of semi-t-operators over S-uninorms

Abstract There are two cases of the (conditional) distributivity of semi-t-operators over S-uninorms that have not been discussed by Fang and Hu in 2019. This paper further characterizes the necessary condition for the left (resp. right) distributivity of semi-t-operators over S-uninorms in these two cases. The sufficient conditions for the left (resp. right) distributivity of semi-t-operators over S-uninorms are also discussed. The outcome of one case is different from the conclusion obtained by Fang and Hu, whereby it is impossible to obtain the necessary and sufficient conditions for semi-t-operators distributed over S-uninorms as usual. In particular, this paper points out that the distributivity of semi-t-operators over S-uninorms is equivalent to their conditional distributivity over S-uninorms under the two cases mentioned above. Some examples are also presented to support our conclusions.

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