A Study of Fundamental Scale for Pairwise Comparisons in Analytical Hierarchy Process

• Main Authors: Guey-Rong Shu, 許桂溶
• Other Authors: Ching-Pu Chen
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/04969225674995602746

碩士 === 國防管理學院 === 國防決策科學研究所 === 91 === The Analytical Hierarchy Process Model was designed by T.L. Saaty as a decision making aid. In order to cluster the decision elements for alternatives, the AHP used pairwise comparison and transferred from oral expression to numerical values-the Fundamental Scale (1-9) to determine the priority. The translation from oral to numerical scale (1-9) which designed by Saaty had some issues about the Systematic Bias. The purpose of this paper is to examine this kind of problem and by using the Accuracy Scale to avoid the bias in consistent test and assessment of the alternatives. The results which carried out by the research are described below: (1) According to the questionnaire, the mean values of the Accuracy Scale are 『1.000, 1.976, 3.384, 5.353, 9.820』 and 『1.000, 1.813, 3.078, 5.098, 9.190』 under the cognitive relative importance which is in the scale with reference and the scale without reference. It is different from the scale (1-9) which designed by Saaty. (2) Comparing to six examples in the Saaty[27], we found that the Consistency Ratio by using the Accuracy Scale is less than using the Saaty’s Scale. This result showed that using Accuracy Scale can achieve better consistency. (3) Random Analysis (a) The value of which is equal to the number of 1.000 will decrease when the matrix expand in 100 random sample sets. The alternatives priority order using Saaty’s Scale and Accuracy Scale are different, the number of difference increases as matrix expansion. Among the optimal alternatives identified by using the Accuracy Scale, there are about 5 to 14 samples sets having different optimal using Saaty’s Scale. (b) To Compare with the Saaty’s Scale, the number of the Consistency Ratio using the Accuracy Scale is less than using Saaty’s Scale increases as the matrix expansion.