Abstract
We introduce a new approach that deals, jointly and in a unified manner, with the topics of numerical (continuous) representability of total preorders and interval orders. This setting is based on the consideration of increasing scales and the systematic use of a particular kind of codomain, that has a key lattice theoretical structure of a completely distributive lattice and allows us to use a single function (taking values in that codomain) in order to represent both kinds of binary relations.
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Bosi, G., Gutiérrez García, J. & Induráin, E. Unified Representability of Total Preorders and Interval Orders through a Single Function: The Lattice Approach. Order 26, 255–275 (2009). https://doi.org/10.1007/s11083-009-9124-x
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DOI: https://doi.org/10.1007/s11083-009-9124-x