General characterizations on the conditional distributivity of semi-t-operators over uninorms

Abstract

In recent years, there are many works about conditional distributivity for aggregation functions, which is closely related to integration theory and utility theory. In this paper, our main idea is to solve conditional distributivity equations from left and right for semi-t-operators over uninorms. One part focuses on these equations involving semi-t-operators over t-norms and obtains some complete characterizations. The other part gives the necessary and sufficient conditions of conditional distributivity for semi-t-operators over uninorms in ${\mathcal{U}}_{max}$ and ${\mathcal{U}}_{min}$ under the condition 0 < U (x, y) <1, which transforms it into the conditional distributivity between t-norms and t-conorms (semi-t-norms and t-conorms, semi-t-conorms and t-norms).