Sufficient conditions for a Heuristic Rating Estimation Method application

TL;DR

This paper establishes the necessary conditions for correctly applying the Heuristic Rating Estimation method, analyzing both arithmetic and geometric algorithms for pairwise comparisons, with illustrative examples demonstrating optimal inconsistency estimations.

Contribution

It formulates the conditions for the proper application of the HRE method across different algorithms and comparison completeness levels.

Findings

Inconsistency estimations in the arithmetic variant are optimal.

Conditions for correct HRE application are explicitly formulated.

Both arithmetic and geometric algorithms are considered for complete and incomplete comparisons.

Abstract

A series of papers has introduced the Heuristic Rating Estimation method, which evaluates a set of alternatives based on pairwise comparisons and the weights of reference alternatives. We formulate the conditions under which the HRE method can be applied correctly. The research considers both arithmetic and geometric algorithms for complete and incomplete pairwise comparison methods. The illustrative examples show that the estimations of inconsistency in the arithmetic variant are optimal.