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**Estimating criterion weights using eigenvectors: A comparative study.**
*(English)*
Zbl 0618.90046

In addition to Saaty’s eigenvector there are infinitely many eigen weight vectors which can be constructed for any given data of estimated weight ratios. As the judgement of the ratios are dependent on personal experience, learning, situations and state of mind, inconsistencies and degree of easiness or confidence to make the judgement on the ratios may be different. Assuming that the confidence in making judgement on these individual ratios can be different, we study the properties of the different eigen weight vectors, including that of T. L. Saaty [”The analytic hierarchy process” (1980; Zbl 0587.90002)] and that recently proposed by K. O. Cogger and P. L. Yu [J. Optimization Theory Appl. 46, 483-491 (1985; Zbl 0552.90050)]. A general framework for the construction of eigen weight vectors incorporating that confidence in obtaining the individual ratios can be different will be proposed and discussed.

### MSC:

90B50 | Management decision making, including multiple objectives |

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\textit{E. Takeda} et al., Eur. J. Oper. Res. 29, 360--369 (1987; Zbl 0618.90046)

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### References:

[1] | Budescu, D.V., Scaling binary comparison matrices: A comment on Narasimhan’s proposal and other methods, Fuzzy sets and systems, 14, (1984) · Zbl 0554.90001 |

[2] | Cogger, K.O.; Yu, P.L., Eigen weight vectors and least distance approximation for revealed preference in pairwise weight ratios, Journal of optimization theory and applications, 36, 4, (1985) · Zbl 0552.90050 |

[3] | Morris, P.C., Weighting inconsistent judgements, Pi mu epsilon journal, (1979) |

[4] | Saaty, T.L., The analytic hierarchy process, (1980), McGraw-Hill New York · Zbl 1176.90315 |

[5] | Saaty, T.L.; Vargas, L.G., The logic of priorities, (1982), Kluwer-Nijhoff Boston · Zbl 0792.92007 |

[6] | Zimbardo, P.G.; Ruch, F.L., Psychology and life, (1975), Scott, Foresman and Company Glenview, IL |

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