  Pairwise comparisons are a well-known method for modelling of the subjective
preferences of a decision maker. A popular implementation of the method is
based on solving an eigenvalue problem for M - the matrix of pairwise
comparisons. This does not take into account the actual values of preference.
The Heuristic Rating Estimation (HRE) approach is a modification of this method
in which allows modelling of the reference values. To determine the relative
order of preferences is to solve a certain linear equation system defined by
the matrix A and the constant term vector b (both derived from M). The article
explores the properties of these equation systems. In particular, it is proven
that for some small data inconsistency the A matrix is an M-matrix, hence the
equation proposed by the HRE approach has a unique strictly positive solution.

Discrete Mathematics