A heuristic rating estimation algorithm for the pairwise comparisons method

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 are a priori known and fixed, whilst the estimates for the others (unknown concepts C U ) need to be computed. The relationship between the local estimation error, understood as the average absolute error E(c) over all direct estimates for the concept 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.

Erratum to: A heuristic rating estimation algorithm for the pairwise comparisons method

“…Remark 1 Like the conditions Q 2 and Q 3 presented in Kułakowski (2015), also Q (i) has the form of the sum of entries of A. Due to this fact, the conclusions formulated in the paragraph following [Kułakowski 2015, (48)] still remain valid.…”

“…The equation system [Kułakowski 2015, (42)] describing the iterative updates of priorities carried out by the algorithm (Kułakowski 2015, Listing 1) can be written as:…”

“…7) computed under the assumptions of the numerical example (Kułakowski 2015, Sect. 5 Further information on the Heuristic Rating Estimation approach, including the criteria given above and a discussion on the convergence, can be found in Kułakowski (2014). Also in the formulas (2), (25) and (33), the summation should start from i = 1 instead of i = 0.…”

Sustainable Street Lighting Design Supported by Hypergraph-Based Computational Model

“…In the fist one, a criterion corresponds to some non-quantitative property, e.g., related to the aesthetics or other subjective characteristics. The ordering by non-quantitative properties may be accomplished using pairwise comparison methods [21], which will not be considered here. In the second case, one deals with measurable parameters.…”

Important Facts and Observations about Pairwise Comparisons (the special issue edition)

“…Ranking with a reference set of alternatives, as in [47,48], is an example of such explorations. To pair or not to pair is not the question.…”