Facets of linear signed order polytopes.
In some decision problems a subset of items from a set \(S\) of \(n\) candidates should be selected. Since the ranking of all feasible subsets in order of preference is often impractical, weaker assumptions are considered. A signed order for \(S\) is a transitive, complete, and self-reflecting binary relation on \(S \cup S^*\), where \(S^*\) is a disjoint copy of \(S\). The linear signed order polytopes are defined and equation systems specifying all facets are presented for \(n \leq 4\). It is shown, that information extracted from the linear signed polytopes can be used for subset comparison.
scientific article; zbMATH DE number 2006365