1 / 23

Analytic Hierarchy Process (AHP) 層級程序分析法

Analytic Hierarchy Process (AHP) 層級程序分析法. Introduction. AHP 系統化複雜的問題 根據不同的層面給予層級分解 每一層最多 7 個項目 量化 提供選擇適當的方案 減少決策錯誤的風險性 . Work Step. Constructing Hierarchies Pair-wise Comparisons Ratio Scales Synthesis of Priorities. Constructing Hierarchies. Constructing Hierarchies (cont.).

salaam
Télécharger la présentation

Analytic Hierarchy Process (AHP) 層級程序分析法

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Analytic Hierarchy Process (AHP)層級程序分析法

  2. Introduction • AHP系統化複雜的問題 • 根據不同的層面給予層級分解 • 每一層最多7個項目 • 量化 • 提供選擇適當的方案 • 減少決策錯誤的風險性

  3. Work Step • Constructing Hierarchies • Pair-wise Comparisons • Ratio Scales • Synthesis of Priorities

  4. Constructing Hierarchies

  5. Constructing Hierarchies (cont.) • Structure the decision problem in a hierarchy • Max 7 criteria in a layer • Stability • Flexibility

  6. Pair-wise Comparisons • Comparison of the alternatives based on the criteria Ratio Scales

  7. Pair-wise Comparisons • Ratio Example: • S11>S22>S33>S12>S13>S23 • R(S11, S11) = 1 • R(S11, S22) = 2 • R(S11, S33) = 3 • R(S11, S12) = 5 • R(S11, S13) = 7 • R(S11, S23) = 9

  8. Pair-wise Comparisons (cont.) • Judge Matrix: • rij>0 • rii=1 • rji=1/rij

  9. Pair-wise Comparisons (cont.) • Judge Matrix Example: S11>S22>S33>S12>S13>S23

  10. Pair-wise Comparisons (cont.) • Ex: • S33 > S22 = S23 > S11 = S12 = S13 • R(S33, S33) = 1 • R(S33, S22) = 5 • R(S33, S23) = 5 • R(S33, S11) = 9 • R(S33, S12) = 9 • R(S33, S13) = 9 R(S22, S23) = 1 R(S22, S11) = 5 R(S22, S12) = 5 R(S22, S13) = 5 R(S11, S12) = 1 R(S11, S13) = 1

  11. Pair-wise Comparisons (cont.) • Judge Matrix Example: • S33 > S22 = S23 > S11 = S12 = S13

  12. Pair-wise Comparisons (cont.) • 計算最大特徵值 (eigenvalue)與特徵向量(eigenvector) • 特徵值 • 特徵向量 W • 特徵向量歸一 • n維運算……n>2,太複雜, for handoff 不好 • 近似值求解 • 行向量和歸一方法, • 不一致的矩陣, 精準度高

  13. 行向量和歸一方法 • 求行向量和 Tj • 求權重Wi

  14. 行向量和歸一方法(cont.) • Example: Judge Matrix

  15. 行向量和歸一方法(cont.) • 求AW

  16. 行向量和歸一方法(cont.) • 求最大特徵值 • 一致性檢定(consistency) • 一致性指標CI(Consistency Index) • CI <0.1 • 不一致, 表示矩陣尺度要重調

  17. 行向量和歸一方法(cont.) • 一致性比率CR (Consistency Ratio) • CR<0.1 • RI: 隨機指標

  18. 矩陣階數n 1 2 3 4 5 6 7 8 R.I. 0 0 0‧58 0‧90 1‧12 1‧24 1‧32 1‧41 矩陣階數n 9 10 11 12 13 14 15 16 R.I. 1‧45 1‧49 1‧51 1‧48 1‧56 1‧57 1‧59 2‧01 一致性測定 理想的評比值會使得Ａｉｊ=Ｗｉ／Ｗｊ，但實際的情況下可能會Ａij≠Ｗi/Ｗj， 因此λmax≠n。所以由λmax與n兩者之間的差異程度可作為判斷一致性高低的 評量準則。一致性指標（Consistency Index，簡稱C.I.）每個成對比較矩陣可查 到對應的隨機指標值（Random Index，簡稱R.I.） 資料來源：Thomas L, Saaty，1991，The Analytic Hierarchy Process，p21

  19. 行向量和歸一方法(cont.)

  20. Synthesis of Priorities • 整合 • 總加權值 其中，i=1…n，(共有n個決策因素) j=1…m，(共有m個替代方案) Wi=第i個criteria之權重 Yij=第j個替代方案中 第i個因素所獲得的評估值

  21. Example • Alternatives: Judge Matrix

  22. Example (cont.)

  23. Example (cont.) • 總加權值

More Related