Fuzzy relational equations on complete Brouwerian lattices

This paper deals with the problem of solving fuzzy relational equations with image composition on complete Brouwerian lattices under finite domains (resp. countably infinite domains). When the right-hand sides of fuzzy relational equations are meet-irreducible elements or have irredundant finite meet-decompositions, some necessary and sufficient conditions for attainable solutions (resp. unattainable solutions) are formulated and some properties of the attainable solutions (resp. the unattainable solutions) are shown. Further, the solution sets are given when they are nonempty.