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A heuristic rating estimation algorithm for the pairwise comparisons method

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  • Konrad Kułakowski

Abstract

The pairwise comparisons method is a powerful tool used for establishing the relative order between different concepts in situations in which it is difficult (or sometimes even impossible) to provide explicit rating. Appropriate ratings are determined by solving eigenvalue problem for the pairwise comparisons matrix. This study presents a new iterative heuristic rating estimation algorithm that tries to deal with the situation when exact estimations for some concepts (stimulus) $$C_{K}$$ C K are a priori known and fixed, whilst the estimates for the others (unknown concepts $$C_{U}$$ C U ) need to be computed. The relationship between the local estimation error, understood as the average absolute error $$E(c)$$ E ( c ) over all direct estimates for the concept $$c\in C_{U}$$ c ∈ C U and the pairwise comparisons matrix inconsistency index is shown. The problem of convergence of subsequent intermediate results is discussed and the convergence conditions are given. Copyright The Author(s) 2015

Suggested Citation

  • Konrad Kułakowski, 2015. "A heuristic rating estimation algorithm for the pairwise comparisons method," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(1), pages 187-203, March.
    • Handle: RePEc:spr:cejnor:v:23:y:2015:i:1:p:187-203
    DOI: 10.1007/s10100-013-0311-x
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    References listed on IDEAS

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    1. George L. Peterson & Thomas C. Brown, 1998. "Economic Valuation by the Method of Paired Comparison, with Emphasis on Evaluation of the Transitivity Axiom," Land Economics, University of Wisconsin Press, vol. 74(2), pages 240-261.
    2. Jozsef Temesi, 2006. "Consistency of the decision-maker in pair-wise comparisons," International Journal of Management and Decision Making, Inderscience Enterprises Ltd, vol. 7(2/3), pages 267-274.
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