| Title:
|
Consistency-driven approximation of a pairwise comparison matrix (English) |
| Author:
|
Dopazo, Esther |
| Author:
|
González-Pachón, Jacinto |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
5 |
| Year:
|
2003 |
| Pages:
|
[561]-568 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The pairwise comparison method is an interesting technique for building a global ranking from binary comparisons. In fact, some web search engines use this method to quantify the importance of a set of web sites. The purpose of this paper is to search a set of priority weights from the preference information contained in a general pairwise comparison matrix; i.e., a matrix without consistency and reciprocity properties. For this purpose, we consider an approximation methodology within a distance-based framework. In this context, Goal Programming is introduced as a flexible tool for computing priority weights. (English) |
| Keyword:
|
ranking theory |
| Keyword:
|
pairwise comparison |
| Keyword:
|
distance-based methods |
| Keyword:
|
goal programming |
| MSC:
|
90B50 |
| MSC:
|
90C29 |
| MSC:
|
91B08 |
| idZBL:
|
Zbl 1249.91025 |
| idMR:
|
MR2042341 |
| . |
| Date available:
|
2009-09-24T19:56:44Z |
| Last updated:
|
2015-03-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135555 |
| . |
| Reference:
|
[1] Brin S., Page L.: The anatomy of a large-scale hypertextual web search engine.Computer Networks and ISDN Systems 30 (1998), 107–117 10.1016/S0169-7552(98)00110-X |
| Reference:
|
[2] Charnes A., Cooper W. W.: Goal programming and multiple objective optimization: Part 1.European J. Oper. Res. 1 (1977), 39–54 MR 0452646, 10.1016/S0377-2217(77)81007-2 |
| Reference:
|
[3] Chu M. T.: On the optimal consistent approximation to pairwise comparison matrices.Linear Algebra Appl. 272 (1998), 155–168 Zbl 0905.62005, MR 1489384 |
| Reference:
|
[4] González-Pachón J., Romero C.: Distance-based consensus methods: a goal programming approach.Omega 27 (1999), 341–347 10.1016/S0305-0483(98)00052-8 |
| Reference:
|
[5] Ignizio J. P., Cavalier T. M.: Linear Programming.Prentice-Hall, Englewood Cliffs, N.J. 1994 |
| Reference:
|
[6] Jensen R. E.: An alternative scaling method for priorities in hierarchical structures.J. Math. Psychology 28 (1984), 317–332 10.1016/0022-2496(84)90003-8 |
| Reference:
|
[7] Kendall M. G.: Further contributions to the theory of paired comparisons.Biometrics 11 (1955), 43–62 MR 0075506, 10.2307/3001479 |
| Reference:
|
[8] Koczkodaj W., Orlowski M.: Computing a consistent approximation to a generalized pairwise comparisons matrix.Comput. Math. Appl. 37 (1999), 79–85 Zbl 0936.65057, MR 1674423, 10.1016/S0898-1221(99)00048-6 |
| Reference:
|
[9] Romero C.: Handbook of Critical Issues in Goal Programming.Pergamon Press, London 1991 Zbl 0817.68034 |
| Reference:
|
[10] Saaty T. L.: The Analytic Hierarchy Process.McGraw-Hill, New York 1980 Zbl 1184.90094, MR 0773297 |
| Reference:
|
[11] Saaty T. L., Vargas L. G.: Comparison of eigenvalues, logarithmic least square and least square methods in estimating ratios.Math. Model. 5 (1984), 309–324 MR 0781652, 10.1016/0270-0255(84)90008-3 |
| Reference:
|
[12] Wei T. H.: The Algebraic Foundations of Ranking Theory.Cambridge Univ. Press, Cambridge 1952 |
| . |
