On the impact of sup‐compositions in the resolution of multi‐adjoint relation equations

Abstract

Multi‐adjoint relation equations are defined by means of a sup‐composition operator involving different conjunctions. Former works reveal that the resolution of a multi‐adjoint relation equation is closely related to such conjunctions. This paper presents a first approach on the study of the influence of the selection of a sup‐composition operator in different aspects of multi‐adjoint relation equations, as their solvability or the extremal elements of their solution set. The obtained results are illustrated by an example concerning multi‐adjoint logic programming. Last but not least, a procedure for reducing the computation of the solution set when only the sup‐composition operator is modified is also introduced.