On the (numerical) ranking associated with any finite binary relation

We generalize the concept of a ‘ranking associated with a linear order’ from linear orders to arbitrary finite binary relations. Using the concept of differential of an object in a binary relation as theoretical primitive, we axiomatically introduce several measurement scales, some of which include the generalized ranking as a special case. We provide a computational formula for this generalized ranking, discuss its many elegant properties and offer some illustrating examples.