Strengthened conditional distributivity of semi-t-operators over uninorms

Abstract

The conditional distributivity of aggregation operations, that is distributivity observed under additional condition imposed on the domain of aggregation operations, is an important property that is highly useful in various theoretical and practical areas, such as the decision-making theory and the integration theory. Therefore, the topic this paper is this restricted distributivity. For this research, the aggregation operations in question are continuous semi-t-operators and uninorms from class Umax∪ Umin with continuous underlying t-norms and t-conorms. The full characterization of distributive pairs of this type is given. The presented research is an extension and upgrade of previously obtained results.