On the Effects of Conjunctions in the Solution Set of Multi-adjoint Fuzzy Relation Equations

A multi-adjoint fuzzy relation equation is defined from a sup-composition operator, which combines different conjunctions. The choice of such compositions has a direct impact on the resolution of the equation. This paper presents a first approach to the consequences of modifying the sup-composition associated with a multi-adjoint fuzzy relation equation in its solution set. Firstly, we show that greater conjunctions lead to lower greatest solutions. Then, two counterexamples are presented to highlight that, in general, an existing ordering in the conjunctions does not lead to comparable minimal solutions. Nevertheless, if the minimal solutions are comparable, we show that greater conjunctions lead to lower minimal solutions.