Quantifying Complexity of Partially Ordered Sets

Guillermo Restrepo ()
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Guillermo Restrepo: Universidad de Pamplona, Interdisciplinary Research Institute

Chapter Chapter 5 in Multi-indicator Systems and Modelling in Partial Order, 2014, pp 85-103 from Springer

Abstract: Abstract We discuss two complexity indicators reported in the literature for partially ordered sets (posets), the first one based on linear extensions and the second one on incomparabilities. Later, we introduce a novel indicator that combines comparabilities and incomparabilities with a Shannon’s entropy approach. The possible values the novel complexity indicator can take are related to the partitions of the number of order relationships through Young diagrams. Upper and lower bounds of the novel indicator are determined and analysed to yield a normalised complexity indicator. As an example of application, the complexity is calculated for the ordering of countries based on their performance in chemical research. Finally, another complexity indicator is outlined, which is based on comparabilities, incomparabilities, and equivalences.

Keywords: Young Diagram; Total Order; Linear Extension; Average Citation; Academic Ranking (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-8223-9_5

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DOI: 10.1007/978-1-4614-8223-9_5

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