Heuristic rating estimation - geometric approach

TL;DR

This paper introduces a geometric heuristic approach for Heuristic Rating Estimation that guarantees solutions regardless of inconsistency levels, expanding applicability over previous methods.

Contribution

It proposes a new geometric heuristic for HRE that ensures solution existence independently of pairwise comparison inconsistency.

Findings

Solution always exists with the geometric approach

Applicable to a broader range of problems

Demonstrated with numerical examples

Abstract

Heuristic Rating Estimation (HRE) is a newly proposed method supporting decisions analysis based on the use of pairwise comparisons. It allows that the ranking values of some alternatives (herein referred to as concepts) are initially known, whilst the ranks for the 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 priorities of all the other concepts. It has been shown that the problem has admissible solution if the inconsistency of pairwise comparisons is not too high. The proposed approach adopts the heuristics according to which to determine the missing priorities a weighted geometric mean is used. In this approach, despite an increased complexity, the solution always exists and their existence does not depend on the inconsistency of the input matrix. Thus, the presented approach might be appropriate for a larger number of problems than the previous method. The formal definition of the proposed geometric heuristics is accompanied by two numerical examples.