具不確定成對比較值的分析曾級統計模式

A Statistical Model on Pairwise Comparisons Under Uncertainty in The Analytic Hierarchy Process

張保隆(Pao-Long Chang) ； 鄭文英(Wen-Ying Jeng)

《管理科學學報》 6卷1期 (1989/05) Pp. 17-25

https://doi.org/10.6504/JOMS.1989.06.01.02

摘要

分析層級程序法，利用成隊比較的方式，求出方案權重的相對重要性，做為方案的選擇標準。雖然一致性比例的求算可以檢查所得結果是否具一致性，但人類進行比較時，通常僅以一概略值陳述比較結果，因此當所求得的方案權重差異微小時，常無足夠信心論斷最佳方案。本文嘗試以隨機誤差來衡量成對比較上的不確定性，利用層級架構中關聯層級的串合，建構層級架構的統計模型，以求算方案權重的估計誤差，在透過統計上假定檢定、區間估計及變異係數等，制定決策法則。

並列摘要

The Analytic Hierarchy Process performs paired comparisons to derive a scale of relative importance for alternatives and uses it as the criterion of making a choice. Although the consistency ratio of the matrix of pairwise comparison provides a means to prevent inconsistent conclusions, it does not include the uncertainty of judgment. As a rule, people often describe their judgment in an approximate manner, therefore, when the weight of alternatives differ only in a narrow margin, one would not have enough confidence in choosing the best alternative. The purpose of this paper is to introduce random error as a measurement of uncertainty in pairwise comparisons. With the hierarchical property of the problem, we construct a statistical model of AHP and calculate the error estimates in the composite weights of alternatives. Finally, notions of hypothesis testing and coefficient of variation are utilized to make a rule for decision