The solution sets of infinite fuzzy relational equations with sup-conjunctor composition on complete distributive lattices

This paper deals with sup-conjunctor composition fuzzy relational equations in infinite domains and on complete distributive lattices. When its right-hand side is a continuous join-irreducible element or has an irredundant continuous join-decomposition, a necessary and sufficient condition describing an attainable solution (resp. an unattainable solution) is formulated and some properties of the attainable solution (resp. the unattainable solution) are shown. Further, the structure of solution sets is investigated.