Abstract Bipolar fuzzy relation equations with join-irreducible right-hand side have been recently studied in the literature, considering a complete distributive residuated lattice endowed with an involutive negation as the underlying algebraic structure. This manuscript elevates the study of these equations to the multi-adjoint paradigm, by significantly weakening the underlying algebraic structure and allowing the use of conjunctions of adjoint pairs instead of triangular norms. Specifically, the resolution of systems of bipolar multi-adjoint relation equations with join-irreducible right-hand side is investigated, the whole solution set is determined, paying particular attention to maximal and minimal solutions, and different examples illustrating the theoretical development are given.
Cornejo et al. (Mon,) studied this question.