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Heuristic rating estimation: geometric approach

Author

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  • Konrad Kułakowski
  • Katarzyna Grobler-Dębska
  • Jarosław Wąs

Abstract

Heuristic rating estimation is a newly proposed method that supports decisions analysis based on the use of pairwise comparisons. It allows the ranking values of some alternatives (herein referred to as concepts) to be initially known, whilst ranks for other concepts have yet to be estimated. To calculate the missing ranks it is assumed that the priority of every single concept can be determined as the weighted arithmetic mean of the priorities of all the other concepts. It has been shown that the problem has an admissible solution if the inconsistency of the pairwise comparisons is not too high. The proposed approach adopts heuristics according to which a weighted geometric mean is used to determine the missing priorities. In this approach, despite increased complexity, a solution always exists and its existence does not depend on the inconsistency or reciprocity of the input matrix. Thus, the presented approach might be appropriate for a larger number of problems than previous methods. Moreover, it turns out that the geometric approach, as proposed in the article, can be optimal. The optimality condition is presented in the form of a corresponding theorem. A formal definition of the proposed geometric heuristics is accompanied by two numerical examples. Copyright The Author(s) 2015

Suggested Citation

  • Konrad Kułakowski & Katarzyna Grobler-Dębska & Jarosław Wąs, 2015. "Heuristic rating estimation: geometric approach," Journal of Global Optimization, Springer, vol. 62(3), pages 529-543, July.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:3:p:529-543
    DOI: 10.1007/s10898-014-0253-4
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    References listed on IDEAS

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    1. Matteo Brunelli & Luisa Canal & Michele Fedrizzi, 2013. "Inconsistency indices for pairwise comparison matrices: a numerical study," Annals of Operations Research, Springer, vol. 211(1), pages 493-509, December.
    2. 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.
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    4. Alessio Ishizaka & Markus Lusti, 2006. "How to derive priorities in AHP: a comparative study," 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. 14(4), pages 387-400, December.
    5. Thomas L. Saaty, 2005. "The Analytic Hierarchy and Analytic Network Processes for the Measurement of Intangible Criteria and for Decision-Making," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 345-405, Springer.
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    1. Kułakowski, Konrad, 2018. "Inconsistency in the ordinal pairwise comparisons method with and without ties," European Journal of Operational Research, Elsevier, vol. 270(1), pages 314-327.
    2. Kułakowski, Konrad & Mazurek, Jiří & Ramík, Jaroslav & Soltys, Michael, 2019. "When is the condition of order preservation met?," European Journal of Operational Research, Elsevier, vol. 277(1), pages 248-254.

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