Sup-t-norm and inf-residuum are a single type of relational equations

We show that the sup-t-norm and inf-residuum types of fuzzy relational equations, considered in the literature as two different types, are in fact two particular instances of a single, more general type of equations. We demonstrate that several pairs of corresponding results on the sup-t-norm and inf-residuum types of equations are simple consequences of single results regarding the more general type of equations. We also show that the new type of equations subsumes other types of equations such as equations with constraints on solutions examples of which are fuzzy relational equations whose solutions are required to be crisp (ordinary) relations.