A simplified implementation of the least squares solution for pairwise comparisons matrices

This is a follow up to "Solution of the least squares method problem of pairwise comparisons matrix" by Bozóki published by this journal in 2008. Familiarity with this paper is essential and assumed. For lower inconsistency and decreased accuracy, our proposed solutions run in seconds instead of days. As such, they may be useful for researchers willing to use the least squares method (LSM) instead of the geometric means (GM) method

A simplified implementation of the least squares solution for pairwise comparisons matrices

This is a follow up to "Solution of the least squares method problem of pairwise comparisons matrix" by Bozóki published by this journal in 2008. Familiarity with this paper is essential and assumed. For lower inconsistency and decreased accuracy, our proposed solutions run in seconds instead of days. As such, they may be useful for researchers willing to use the least squares method (LSM) instead of the geometric means (GM) method

The limit of inconsistency reduction in pairwise comparisons

This study provides a proof that the limit of a distance-based inconsistency reduction process is a matrix induced by the vector of geometric means of rows when a distance-based inconsistent pairwise comparisons matrix is transformed into a consistent PC matrix by stepwise inconsistency reduction in triads. The distance-based inconsistency indicator was defined by Koczkodaj (1993) for pairwise comparisons. Its convergence was analyzed in 1996 (regretfully, with an incomplete proof) and finally completed in 2010. However, there was no interpretation provided for the limit of convergence despite its considerable importance. This study also demonstrates that the vector of geometric means and the right principal eigenvector are linearly independent for the pairwise comparisons matrix size greater than three, although both vectors are identical (when normalized) for a consistent PC matrix of any size

Use of Pairwise Comparison Method in Road-and-Bridge Tenders

The paper is a brief presentation of the pairwise comparison (PC) method, implemented with the use of the Concluder, a modern tool for PC analysis which is being developed by Professor Waldermar Koczkodaj and which is used for comparing tenders in the road-and-bridge construction industry. The paper discusses the tender criteria which are adopted for tenders in this industry. It addresses the issue of developing the relevant weights while using one of the functions of the expert system, i.e. the function which relies on the opinions of the experts familiar with a given matter, who however not always present the same views. Once the experts’ opinions have been collected, they can be “agreed” while using the PC method. Diversification of the criteria is particularly important from the point of view of improvement of the quality of the services offered by the road-and-bridge construction industry in Poland, since in to-date practice the price has been the only or the dominant criterion. The paper contains examples (in terms of numbers) of analysis of tender criteria where the price was not the only criterion, which is the starting point for further research

Convergence of inconsistency algorithms for the pairwise comparisons

Abstract A formal proof of convergence of a class of algorithms for reducing inconsistency of pairwise comparisons (PC) method is presented. The design of such algorithms is proposed. The convergence of the algorithms justifies making an inference that iterated modifications of the pc matrix made by human experts should also converge. This is instrumental for credibility of practical applications of the pc method