Notes on the existence of a solution in the pairwise comparisons method using the heuristic rating estimation approach

Konrad Kułakowski
2015 Annals of Mathematics and Artificial Intelligence  
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
more » ... 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.
doi:10.1007/s10472-015-9474-6 fatcat:t2z6pdchffa2vcmoctmy63fvja