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Estimators of the relations of: equivalence, tolerance and preference on the basis of pairwise comparisons with random errors

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  • Leszek Klukowski

Abstract

This paper presents a review of results of the author in the area of estimation of the relations of equivalence, tolerance and preference within a finite set based on multiple, independent (in a stochastic way) pairwise comparisons with random errors, in binary and multivalent forms. These estimators require weaker assumptions than those used in the literature on the subject. Estimates of the relations are obtained based on solutions to problems from discrete optimization. They allow application of both types of comparisons – binary and multivalent (this fact relates to the tolerance and preference relations). The estimates can be verified in a statistical way; in particular, it is possible to verify the type of the relation. The estimates have been applied by the author to problems regarding forecasting, financial engineering and bio-cybernetics.

Suggested Citation

  • 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.
  • Handle: RePEc:wut:journl:v:2:y:2012:p:15-34:id:1048
    DOI: 10.5277/ord120202
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    References listed on IDEAS

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    1. 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.
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    1. repec:wut:journl:v:2:y:2012:id:1048 is not listed on IDEAS
    2. 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.

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