Bipolar multi-adjoint relation equations with join-irreducible right-hand side

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.