Heuristic rating estimation: geometric approach

Konrad Kułakowski (), Katarzyna Grobler-Dębska () and Jarosław Wąs ()

Journal of Global Optimization, 2015, vol. 62, issue 3, 529-543

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

Keywords: Multicriteria analysis; Pairwise comparisons; Ranking theory; AHP; Logarithmic least square method (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-014-0253-4

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