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Quantifying Complexity of Partially Ordered Sets

In: Multi-indicator Systems and Modelling in Partial Order

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  • Guillermo Restrepo

    (Universidad de Pamplona, Interdisciplinary Research Institute
    Universidad de Pamplona, Laboratorio de Química Teórica)

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.

Suggested Citation

  • Guillermo Restrepo, 2014. "Quantifying Complexity of Partially Ordered Sets," Springer Books, in: Rainer Brüggemann & Lars Carlsen & Jochen Wittmann (ed.), Multi-indicator Systems and Modelling in Partial Order, edition 127, chapter 0, pages 85-103, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8223-9_5
    DOI: 10.1007/978-1-4614-8223-9_5
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