I put a preliminary draft (not yet checked for errors) of the article “Orderings of filters in terms of reloids” at Algebraic General Topology site.
The abstract Orderings of filters which extend Rudin-Keisler preorder of ultrafilters are defined in terms of reloids that (roughly speaking) is filters on sets of binary relations between some sets. Also there is defined isomorphism of filters which extends Rudin-Keisler equivalence of ultrafilters.
In the future I will almost certainly integrate that short article into the longer article Funcoids and Reloids.