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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.).

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

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  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

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