%0 Journal Article 
%A Cornejo Piñero, María Eugenia
%A Lobo Palacios, David
%A Medina Moreno, Jesús
%A DeBaets, Bernard
%T Bipolar equations on complete distributive symmetric residuated lattices: The case of a join-irreducible right-hand side
%D 2022
%@ 0165-0114
%U http://hdl.handle.net/10498/26921
%X Bipolar max-∗equations, with ∗a triangular norm, have recently become a popular research topic embedded in the broad field of fuzzy relational equations. In this paper, we lift the work from the restrictive setting of the real unit interval — obfuscating the underlying lattice-theoretical essence — to the general setting of complete distributive symmetric residuated lattices, allowing to build upon the vast body of knowledge on unipolar sup-∗equations on complete distributive residuated lattices. We determine the full solution set, with particular emphasis on the extremal solutions, of a bipolar sup-∗equation in case the right-hand side is a join-irreducible element. The results are illustrated by means of ample examples.
%K Bipolar equation
%K Distributive symmetric residuated lattice
%K Negation operator
%K Irreducible element
%~ Universidad de Cádiz