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Computer Recognition Systems 2 pp 232–241Cite as

Estimation of the Preference Relation on the Basis of Medians from Pairwise Comparisons in the Form of Difference of Ranks

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Part of the book series: Advances in Soft Computing ((AINSC,volume 45))

Abstract

The problem of estimation of the preference relation in a finite set on the basis of medians from multiple pairwise comparisons, in the form of difference of ranks with random errors, with the use of nearest adjoining order idea (NAO), is investigated in the paper. The estimated form of the relation is obtained on the basis of a discrete programming problem; some probabilistic properties of the estimator are determined. They are obtained under weak assumptions about distributions of comparison errors; in particular, the expected value of comparison error of each pair can be different than zero.

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References

  1. David H. A.(1970) Order Statistics. J. Wiley, New York.

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  2. David H. A. (1988) The Method of Paired Comparisons, 2nd ed. Ch. Griffin, London.

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  3. Klukowski L. (1994) Some probabilistic properties of the nearest adjoining order method and its extensions. Annals of Operations Research, 51, 241–261.

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  4. Klukowski L. (2000) The nearest adjoining order method for pairwise comparisons in the form of difference of ranks. Annals of Operations Research, 97, 357–378.

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  5. Klukowski L. (2007a) Estimation of tolerance relation the basis of multiple pairwise comparisons with random errors. Control and Cybernetics, to appear.

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  6. Klukowski L. (2007b) Estimation of preference relation the basis of multiple pairwise comparisons with random errors. Modeling of Preference and Risk’07 Conference in Ustronie, 16-17 April, 2007, Economics University, Katowice, to appear (in Polish).

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  7. Slater P. (1961) Inconsistencies in a schedule of paired comparisons. Biometrika, 48, 303–312.

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Author information

Authors and Affiliations

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

    Leszek Klukowski

Authors
  1. Leszek Klukowski
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Editors and Affiliations

  1. Faculty of Electronics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370, Wroclaw, Poland

    Marek Kurzynski , Edward Puchala , Michal Wozniak  & Andrzej Zolnierek , ,  & 

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© 2007 Springer-Verlag Berlin Heidelberg

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Klukowski, L. (2007). Estimation of the Preference Relation on the Basis of Medians from Pairwise Comparisons in the Form of Difference of Ranks. In: Kurzynski, M., Puchala, E., Wozniak, M., Zolnierek, A. (eds) Computer Recognition Systems 2. Advances in Soft Computing, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75175-5_29

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  • DOI: https://doi.org/10.1007/978-3-540-75175-5_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75174-8

  • Online ISBN: 978-3-540-75175-5

  • eBook Packages: EngineeringEngineering (R0)

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