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Consistency-driven approximation of a pairwise comparison matrix. (English) Zbl 1249.91025

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.

MSC:

91B08 Individual preferences
90B50 Management decision making, including multiple objectives
90C29 Multi-objective and goal programming
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References:

[1] Brin S., Page L.: The anatomy of a large-scale hypertextual web search engine. Computer Networks and ISDN Systems 30 (1998), 107-117
[2] Charnes A., Cooper W. W.: Goal programming and multiple objective optimization: Part 1. European J. Oper. Res. 1 (1977), 39-54 · Zbl 0375.90079
[3] Chu M. T.: On the optimal consistent approximation to pairwise comparison matrices. Linear Algebra Appl. 272 (1998), 155-168 · Zbl 0905.62005
[4] González-Pachón J., Romero C.: Distance-based consensus methods: a goal programming approach. Omega 27 (1999), 341-347
[5] Ignizio J. P., Cavalier T. M.: Linear Programming. Prentice-Hall, Englewood Cliffs, N.J. 1994
[6] Jensen R. E.: An alternative scaling method for priorities in hierarchical structures. J. Math. Psychology 28 (1984), 317-332
[7] Kendall M. G.: Further contributions to the theory of paired comparisons. Biometrics 11 (1955), 43-62
[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
[9] Romero C.: Handbook of Critical Issues in Goal Programming. Pergamon Press, London 1991 · Zbl 0817.68034
[10] Saaty T. L.: The Analytic Hierarchy Process. McGraw-Hill, New York 1980 · Zbl 1184.90094
[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 · Zbl 0584.62102
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