Unified representability of total preorders and interval orders through a single function: the lattice approach
The authors introduce a new approach that deals in a unified manner with the numerical (continuous) representability of total preorders and interval orders. Their method relies on increasing scales and the use of a particular kind of codomain that has the structure of a completely distributive lattice and allows them to use a single function (taking values in that codomain) in order to represent both kinds of binary relations. They state that it remains an open problem to develop a similar theory for semiorders.
scientific article; zbMATH DE number 5603897
scientific article