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This paper addresses the general problem of designing ordinal classificationmethods based on comparing actions with limiting boundaries of ordered classes(categories). The fundamental requirement of the method consists of setting arelational 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, andD is a subset of S. An asymmetric preference relation P is defined from S.Other requirements are imposed on the actions which compose the limitingboundaries between adjacent classes, in such a way that each class is closedbelow and above. The paper proposes S-based and P-based assignment procedures.Each of them is composed of two complementary assignment procedures, whichcorrespond through the transposition operation and should be used conjointly.The methods work under several basic conditions on the set of limitingboundaries. Under other more demanding separability requirements, eachprocedure fulfills the set of structural properties established for otheroutranking-based ordinal classification methods. Our proposal avoids theconflict between the required correspondence through the transpositionoperation and the assignment of limiting actions to the classes to which theybelong. We thus propose very diverse S and P-based ordinal classificationapproaches with desirable properties, which can be designed by using decisionmodels with the capacity to build preference relations fulfilling the basicrequirements to S and D.

a theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes