Bipolar multi-adjoint relation equations as systems of bipolar multi-adjoint sup-equations

Bipolar fuzzy relation equations are fuzzy relation equations enriched with a negation operator, where the unknown relation appears together with its negation. The investigation of this topic is receiving much attention in late years, from a theoretical but also from an applied approach, as it happened in the case of fuzzy relation equations. The development of bipolar fuzzy relation equations, specially from an applied perspective, demands relaxing the underlying requirements of the notion. This leads to the contribution of this paper, where the concept of bipolar multi-adjoint relation equation has been presented, allowing the use of multiple conjunctions in the composition operator. Additionally, a formal procedure to transform a bipolar multi-adjoint relation equation into a set of systems of bipolar multi-adjoint sup-equations has been presented.