On The Conditional Distributivity Of Semi-uninorms Over Uninorms With Continuous Underlying Operators

Based on the fact that the role of aggregation functions is widely recognized from a large number of disciplines of mathematics and natural sciences to economics and social sciences,many researchers pay great attention to the investigation of aggregation functions,one of the main topics in studying aggregation functions from a theoretical perspective is to characterize these aggregation functions with certain properties,these properties are usually derived from the solutions of functional equations involving such functions.One of these properties is conditional distributivity.Semi-uninorms,as a form of relaxed uninorms,is a kind of more general fuzzy aggregation function which has neither commutativity nor associativity,the study of this functions can be used in pseudoanalysis,information aggregation and other practical applications.In the literatures on the conditional distributivity of semiuninorms,most of the research is limited to discussing the conditional distributivity of semi-uninorms over special binary operators,the second operator is a binary operator with neutral element 0 or 1,or a class of uninorm with additional conditions.In the present study,we characterize all solutions of the conditional distributivity equations of semi-uninorms over uninorms with continuous underlying operators,in which semi-uninorms belong to several common classes of semi-uninorms,i.e.,representable semi-uninorms,the semi-uninorms from Nemax ∪ Nemin and continuous semi-uninorms.This study extends previous results by focusing on a much wider class of uninorms.