Interval-valued rank in finite ordered sets. (English) Zbl 1414.06002
The authors consider the rank as a measure of the vertical levels and positions of elements of an ordered set. Representing semantic hierarchies as finite, bounded ordered sets, they recognize the duality of ordered structures to motivate rank functions with respect to verticality both from bottom and from the top. Their rank functions are interval-valuated even for non-graded ordered sets. The concept of rank width arises naturaly, allowing to identify the ordered set region with point-valued width as longest graded portion. The properties of standard interval rank function are examined, including the relationship to traditional grading and rank functions.
Reviewer: Ivan Chajda (Přerov)
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