Infinite fuzzy relational equations with sup-conjunctor on complete Brouwerian lattices

In this paper, a system of infinite fuzzy relational equations with sup-conjunctor on complete Brouwerian lattices is investigated. Some properties of attainable (resp. unattainable, partially attainable) solutions of the system are first shown, which are closely related minimal solutions. Some necessary and sufficient conditions for attainable (resp. minimal) solutions are then represented, and in the end, the set of attainable solutions is given when the right hand sides of the system either are join-irreducible elements or have irredundant finite join-decompositions.