| Summary: | 碩士 === 南台科技大學 === 工業管理研究所 === 97 === The analytic hierarchy process (AHP) is one of the most commonly used multi-attributes decision analysis techniques, for the reason that its implementation steps are similar to commonly used analysis steps of human beings. It is even more popular in cases that quantitative and qualitative attributes combine, for example: in the areas of strategic decision and risk management. In this study, we set out from the meaning of judgment matrix, point out that its coefficients are perturbed measurement data of a preference structure, and then show that Saaty’s eigenvector method for judgment matrix analysis has the following theoretical weakness: (1) the calculation of eigenvector does not accord with the essence meaning of a judgment matrix; (2) the eigenvector method cannot give a sufficient analysis on the effect of experimental error on the priority vector; (3) its assumption that the perturbation in judgment matrix is small enough, may not hold in practical applications. In addition, this method cannot take the ordering relations of priority weights, found in the practice or from the matrix, into consideration. On contrast, the methods based on statistical regression not only can take these ordering relations into consideration, also have nice properties in the decision theory. Therefore, analyzing the judgment matrix by regression is more proper. Moreover, since the judgment matrix is used to represent a preference structure, it can be replaced by a fuzzy relation. Using the cut sets of the associated fuzzy relation, we define the graphical consistency and the graphical consistency constraints of a judgment matrix, then we consider the theoretical properties of the logarithm least squares method and the goal programming method with the graphical consistency constraints, and compare theses two methods with the most commonly used methods.
|
|---|
