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The nearest adjoining order method for pairwise comparisons in the form of difference of ranks

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  • Leszek Klukowski

Abstract

The problem of ranking of elements from some finite set on the basis of nearest adjoining order method for pairwise comparisons is investigated in this paper. It is assumed that in the set under consideration there exists a weak preference relation, which is to be identified (estimated) on the basis of pairwise comparisons in the form of difference of ranks. Moreover, the results of comparisons may be disturbed with random errors; the assumptions made about error distributions are not restrictive. The paper comprises: the problem formulation (definitions, assumptions, and optimisation problem, which provides the NAO solution) and the theoretical background – the form of distributions of random variables which make it possible to determine the properties of NAO solution, in particular, evaluation of the probability, that the NAO solution is equivalent to the errorless one. The approach presented in the paper can be extended to the case of more than one comparison for each pair of elements, i.e., completely formalised multi-experts ranking procedure. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Leszek Klukowski, 2000. "The nearest adjoining order method for pairwise comparisons in the form of difference of ranks," Annals of Operations Research, Springer, vol. 97(1), pages 357-378, December.
    • Handle: RePEc:spr:annopr:v:97:y:2000:i:1:p:357-378:10.1023/a:1018948829280
    DOI: 10.1023/A:1018948829280
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    Cited by:

    1. Leszek Klukowski, 2017. "Determining an estimate of an equivalence relation for moderate and large sized sets," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(2), pages 45-58.
    2. repec:wut:journl:v:2:y:2012:id:1048 is not listed on IDEAS
    3. Leszek Klukowski, 2012. "Estimators of the relations of: equivalence, tolerance and preference on the basis of pairwise comparisons with random errors," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(2), pages 15-34.

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