Sup-t-norm and inf-residuum are one type of relational product: Unifying framework and consequences

We present a simple framework which enables us to consider the well-known sup-t-norm and inf-residuum products of relations as two particular cases of a single, more general type of product. We present basic properties of the framework and consequences for the theory of fuzzy relations. Informally, the paper implies that in many cases of fuzzy relational modeling, such as in solving fuzzy relational equations, there is no need to develop the methods for sup-t-norm and inf-residuum products separately, because these methods are just two particular instances of a single method. © 2011 Elsevier B.V. All rights reserved.