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Proceedings of the 8th International Conference on Computer Recognition Systems CORES 2013 pp 41–52Cite as

Estimation of the Relations of: Equivalence, Tolerance and Preference on the Basis of Pairwise Comparisons

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 226))

Abstract

The paper presents the estimators of three relations: equivalence, tolerance and preference in a finite set on the basis of multiple pairwise comparisons, disturbed by random errors; they have been developed by the author. The estimators can rest on: binary (qualitative), multivalent (quantitative) and combined comparisons. The estimates are obtained on the basis of discrete programming tasks. The estimators require weak assumptions about distributions of comparisons errors, especially allow non-zero expected values. The estimators have good statistical properties, in particular consistency. The paper summarizes the results obtained by the author; the broader view is presented in Klukowski 2011a.

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Author information

Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Leszek Klukowski

Authors
  1. Leszek Klukowski
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Correspondence to Leszek Klukowski .

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Editors and Affiliations

  1. , Department of Systems and Computer, Wroclaw University of Technology, WybrzezeWyspianskiego St 27, Wroclaw, 50-370, Poland

    Robert Burduk

  2. , Department of Systems and Computer, Wroclaw University of Technology, WybrzezeWyspianskiego St 27, Wroclaw, 50-370, Poland

    Konrad Jackowski

  3. , Department of Systems and Computer, Wroclaw University of Technology, WybrzezeWyspianskiego St 27, Wroclaw, 50-370, Poland

    Marek Kurzynski

  4. , Department of Systems and Computer, Wroclaw University of Technology, WybrzezeWyspianskiego St 27, Wroclaw, 50-370, Poland

    Michał Wozniak

  5. , Department of Systems and Computer, Wroclaw University of Technology, WybrzezeWyspianskiego St, Wroclaw, 50-370, Poland

    Andrzej Zolnierek

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Klukowski, L. (2013). Estimation of the Relations of: Equivalence, Tolerance and Preference on the Basis of Pairwise Comparisons. In: Burduk, R., Jackowski, K., Kurzynski, M., Wozniak, M., Zolnierek, A. (eds) Proceedings of the 8th International Conference on Computer Recognition Systems CORES 2013. Advances in Intelligent Systems and Computing, vol 226. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00969-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-00969-8_4

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00968-1

  • Online ISBN: 978-3-319-00969-8

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