Bipolar equations on complete distributive symmetric residuated lattices: The case of a join-irreducible right-hand side

Bipolar max-? equations, with ? a triangular norm, have recently become popular research topic embedded in the broad field of fuzzy relational equations. In this paper, we lift work from restrictive setting real unit interval — obfuscating underlying lattice-theoretical essence to general complete distributive symmetric residuated lattices, allowing build upon vast body knowledge on unipolar sup-? equations lattices. We determine full solution set, particular emphasis extremal solutions, bipolar equation case right-hand side is join-irreducible element. The results are illustrated by means ample examples.