  This paper addresses the general problem of designing ordinal classification
methods based on comparing actions with limiting boundaries of ordered classes
(categories). The fundamental requirement of the method consists of setting a
relational system (D,S), where S and D are reflexive and transitive relations,
respectively, S should be compatible with the order of the set of classes, and
D is a subset of S. An asymmetric preference relation P is defined from S.
Other requirements are imposed on the actions which compose the limiting
boundaries between adjacent classes, in such a way that each class is closed
below and above. The paper proposes S-based and P-based assignment procedures.
Each of them is composed of two complementary assignment procedures, which
correspond through the transposition operation and should be used conjointly.
The methods work under several basic conditions on the set of limiting
boundaries. Under other more demanding separability requirements, each
procedure fulfills the set of structural properties established for other
outranking-based ordinal classification methods. Our proposal avoids the
conflict between the required correspondence through the transposition
operation and the assignment of limiting actions to the classes to which they
belong. We thus propose very diverse S and P-based ordinal classification
approaches with desirable properties, which can be designed by using decision
models with the capacity to build preference relations fulfilling the basic
requirements to S and D.
