Convergence of inconsistency algorithms for the pairwise comparisons. (English) Zbl 0875.68472
Summary: 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.
MSC:
| 68W10 | Parallel algorithms in computer science |
Keywords:
Design of algorithms; Analysis of algorithms; Iterative algorithms; Algorithm convergence; Performance evaluation; Local and global triad inconsistencySoftware:
ConcluderReferences:
| [1] | Crawford, G., The geometric mean procedure for estimating the scale of judgement matrix, Math. Model., 9, 327-334 (1987) · Zbl 0624.62108 |
| [2] | Duszak, Z.; Koczkodaj, W. W., The generalization of a new definition of consistency for pairwise comparisons, Inform. Process. Lett., 52, 273-276 (1994) · Zbl 0815.68084 |
| [3] | Herman, M.; Koczkodaj, W. W., Monte Carlo study of pairwise comparisons, Inform. Process. Lett., 57, 25-29 (1996) · Zbl 1004.68550 |
| [4] | Gantmacher, F. R., Applications of the Theory of Matrices (1959), Interscience: Interscience New York · Zbl 0085.01001 |
| [5] | Jense, R. E., An alternative scaling method for priorities in hierarchical structures, J. Math. Psychology, 28, 317-332 (1984) |
| [6] | Koczkodaj, W. W., A new definition of consistency of pairwise comparisons, Math. Comput. Modelling, 18, 79-84 (1993) · Zbl 0804.92029 |
| [7] | Koczkodaj, W. W., Statistically accurate evidence of improved error rate by pairwise comparisons, Perceptual and Motor Skills, 82, 43-48 (1996) |
| [8] | Saaty, T. L., A scaling methods for priorities in hierarchical structure, J. Math. Psychology, 15, 234-281 (1977) · Zbl 0372.62084 |
| [9] | Saaty, T. L.; Vargas, L. G., Comparison of eigenvalue,logarithmic least square and least square methods in estimating ratios, Math. Model., 5, 309-324 (1984) · Zbl 0584.62102 |
| [10] | Thurstone, L. L., A law of comparative judgments, Psychological Rev., 34, 273-286 (1927) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
