Aggregation Operators and Distributivity Equations

Abstract

Aggregation operators are an important mathematical tool in a number of areas and disciplines of both pure and applied mathematics. For both theoretical and practical reasons, aggregation operators with an annihilator and aggregation operators with a neutral element are of special interest for researchers. The issue of distributivity of aggregation operators is crucial for many different areas such as decision making theory and integration theory. This chapter covers the characterization of all pairs (F, G) of aggregation operators that satisfy distributivity law, on both whole and restricted domains, where F is a T-uninorm in $\mathsf {U}_{\max }$ or a nullnorm with the annihilator $a\in ]0,1[$, and G is a t-conorm or a uninorm from the classes $\mathsf {U}_{\min }$ or $\mathsf {U}_{\max }$.