An orthogonal basis for computing a consistent approximation to a pairwise comparison matrix. (English) Zbl 0903.68218
Summary: The algorithm for finding a consistent approximation to an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric. An orthogonal basis is introduced in the vector space formed by the images of consistent matrices. The required consistent approximation is the orthogonal projection of the transformed matrix onto this space.
MSC:
| 65F30 | Other matrix algorithms (MSC2010) |
Software:
ConcluderReferences:
| [1] | Koczkodaj, W. W., A new definition of consistency of pairwise comparisons, Mathl. Comput. Modelling, 18, 7, 79-84 (1993) · Zbl 0804.92029 |
| [2] | Holsztynski, W.; Koczkodaj, W. W., Convergence analysis of inconsistency algorithms for the pairwise comparisons method, Information Processing Letters, 59, 4, 197-202 (1996) · Zbl 0875.68472 |
| [3] | Fechner, G. T., (Elements of Psychophysics, Volume 1 (1965), Holt, Rinehart & Winston: Holt, Rinehart & Winston New York), translation by H.E. Adler of Elemente der Psychophysik, (1860) |
| [4] | Thurstone, L. L., A law of comparative judgments, Psychological Reviews, 34, 273-286 (1927) |
| [5] | Saaty, T. L., A scaling method for priorities in hierarchical structure, Journal of Mathematical Psychology, 15, 3, 234-281 (1977) · Zbl 0372.62084 |
| [6] | (Behnke, H.; etal., Fundamentals of Mathematics, Volume 11 (1987), MIT Press) |
| [7] | Koczkodaj, W. W.; Mackasey, W. O., Mineral-potential assessment by consistency-driven pairwise comparisons, Exploration and Mining Geology, 6, 1 (1997), (to appear) |
| [8] | Jensen, R. E., An alternative scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology, 28, 317-332 (1984) |
| [9] | Herman, M.; Koczkodaj, W. W., Monte Carlo study of pairwise comparisons, Information Processing Letters, 57, 1, 25-29 (1996) · Zbl 1004.68550 |
| [10] | Koczkodaj, W. W., Statistically accurate evidence of improved error rate by pairwise comparisons, Perceptual and Motor Skills, 82, 43-48 (1996) |
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.
