Left and right distributivity equations for semi-t-operators and uninorms

Abstract

Recently, the distributivity equation for different kind of operators has become a focus of research as the crucial tool in the numerous applications as utility and optimization theory, or integration theory. The main purpose of this paper is to study the distributivity equations between two special classes of aggregation operators namely, semi-t-operators and uninorms. Without the commutativity assumption of semi-t-operators it is necessary to consider the left and the right distributivity conditions separately. In both cases, the obtained solutions are significantly different.