On the correspondence between reciprocal relations and strongly complete fuzzy relations

Fuzzy relations and reciprocal relations are two popular tools for representing degrees of preference. It is important to note that they carry a different semantics and cannot be equated directly. We propose a simple transformation based on implication operators that allows to establish a one-to-one correspondence between both formalisms. It sets the basis for a common framework in which properties such as transitivity can be studied and definitions belonging to different formalisms can be compared. As a byproduct, we propose a new family of upper bound functions for cycle-transitivity. Finally, we unveil some interesting equivalences between types of transitivity that were left uncompared till now.