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**Eigen weight vectors and least-distance approximation for revealed preference in pairwise weight ratios.**
*(English)*
Zbl 0552.90050

A new eigenweight vector is derived for the data of pairwise weight ratios. The well-known eigenweight vector derived by T. L. Saaty [”The analytic hierarchy process”, New York (1980)] is then compared and contrasted in the light of least-distance approximation models. It is shown that the new eigenweight vector commands advantages over saaty’s, including less rigid assumptions on the error terms, robustness of solution, in addition to the fact that the new eigenweight vector can be computed very easily. The reader can construct other types of eigenweight vectors and least-distance approximation models using the framework of this article.

### MSC:

90B50 | Management decision making, including multiple objectives |

91B06 | Decision theory |

91B08 | Individual preferences |

### Keywords:

revealed preference; eigenweight vector; pairwise weight ratios; least- distance approximation models; multiple criteria
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\textit{K. O. Cogger} and \textit{P. L. Yu}, J. Optim. Theory Appl. 46, 483--491 (1985; Zbl 0552.90050)

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### References:

[1] | Keeney, R. L., andRaiffa, H.,Decisions with Multiple Objectives: Preferences and Value Tradeoffs, John Wiley and Sons, New York, New York, 1976. |

[2] | Barron, F. H., andPerson, H. B.,Assessment of Multiplicative Utility Functions via Holistic Judgments, Organizational Behavior and Human Performance, Vol. 24, pp. 147-166, 1979. |

[3] | Saaty, T. L.,A Scaling Method for Priorities in Hierarchical Structures, Journal of Mathematical Psychology, Vol. 15, pp. 234-281, 1977. · Zbl 0372.62084 |

[4] | Saaty, T. L.,The Analytic Hierarchy Process, McGraw-Hill, New York, New York, 1980. · Zbl 0587.90002 |

[5] | Chu, A. T. W., Kalaba, R. E., andSpingarn, K.,A Comparison of Two Methods for Determining the Weights of Belonging to Fuzzy Sets, Journal of Optimization Theory and Applications, Vol. 27, pp. 531-538, 1979. · Zbl 0377.94002 |

[6] | Lindsay, P. H., andNorman, D. A.,Human Information Processing: An Introduction to Psychology, Academic Press, New York, New York, 1972. |

[7] | Yu, P. L.,Behavior Bases and Habitual Domains of Human Decision Behavior: An Integration of Psychology, Optimization Theory, and Common Wisdon, International Journal of Systems, Measurement, and Decisions, Vol. 1, pp. 39-62, 1981. |

[8] | Rao, C. R.,Linear Statistical Inference and Its Applications, John Wiley and Sons, New York, New York, 1973. · Zbl 0256.62002 |

[9] | Cogger, K. O., andYu, P. L.,Eigenweight Vectors and Least-Distance Approximation for Revealed Preference in Pairwise Weight Ratios, University of Kansas, Lawrence, Kansas, School of Business, Working Paper No. 162, 1983. |

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