Some Results of Interval-valued fuzzy relational equations with sup-conjunctor composition

This paper investigates the problem of solving sup-conjunctor composite finite interval-valued fuzzy relational equations over complete Brouwerian lattices. First, we introduce the notions of tolerable solution set, united solution set and controllable solution set, respectively and discuss their properties. Secondly, we obtain some necessary and sufficient conditions that these solution sets are nonempty and show the structures of the three types of solution set when the right-hand sides are join-irreducible or irredundant finitely join-decomposable. Finally, we give some numerical examples.