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Determining an estimate of an equivalence relation for moderate and large sized sets

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  • Leszek Klukowski

Abstract

This paper presents two approaches to determining estimates of an equivalence relation on the basis of pairwise comparisons with random errors. Obtaining such an estimate requires the solution of a discrete programming problem which minimizes the sum of the differences between the form of the relation and the comparisons. The problem is NP hard and can be solved with the use of exact algorithms for sets of moderate size, i.e. about 50 elements. In the case of larger sets, i.e. at least 200 comparisons for each element, it is necessary to apply heuristic algorithms. The paper presents results (a statistical preprocessing), which enable us to determine the optimal or a near-optimal solution with acceptable computational cost. They include: the development of a statistical procedure producing comparisons with low probabilities of errors and a heuristic algorithm based on such comparisons. The proposed approach guarantees the applicability of such estimators for any size of set.

Suggested Citation

  • 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.
    • Handle: RePEc:wut:journl:v:2:y:2017:p:45-58:id:1286
    DOI: 10.5277/ord170203
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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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