1. AHP/ANP 2014724

2. 2 9:10-9:30 9:30-12:30 1.AHP 2.AHP AHP AHP 12:30-13:30 13:30-16:30 1.ANP 2.ANP ANP ANP 16:30-17:00 Q&A 3. AHP 9:30~12:30 4. AHP? 4 ABC 5. AHP? 5 (Analytic Hierarchy Process, AHP) A CB D 6. AHP 1926 1947 1953 OR 1957 OR 1963OR 1969 1971AHP 1980AHP 6 Thomas L. Saaty 1926~present 7. AHP 1. () 2. 3. 1. 2. 3. 7 ANP 8. AHP 1. 2. 3. 4. 5. 6. 7. 8. 8 AA CCBB DD A CB D 123 45 678 9. AHP 1. 2. 3. 4. 5. 6. A>B>CA>C AB3 BC2A B6 7. 8. 9 Saaty, T. L., 1980. The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, New York: McGraw-Hill. 10. AHP 10 11. 11 Good! Good! Dorado et al. (2014) An AHP application to select software for engineering education, Computer Applications in Engineering Education, Vol. 22, No. 2, pp.200-208. Nefeslioglu et al.(2013) "A modified analytical hierarchy process (M-AHP) approach for decision support systems in natural hazard assessments," Computers & Geosciences, Vol. 59, pp. 1-8. 12. 12 1 2 3 4 13. 13 612 612 1~2 1~2 14. 14 15. 15 a1 a2 ,, an a1 a2 ,, an AA CCBB DD b1 b2 ,, bn b1 b2 ,, bn c1 c2 ,, cn c1 c2 ,, cn d1 d2 ,, dn d1 d2 ,, dn a1 a2 ,, an A CB D b1 b2 ,, bn c1 c2 ,, cn d1 d2 ,, dn Delphi 16. 16 17. 17 1 2 3 4 18. Delphi 18 N N ~ 19. Delphi 75% 0.60.6~1 1 OOO (5)(4)(3)(2) (1) 1 5 4.3 0.72 2 4 4.13 0.59 3 5 4.12 0.44 4 4 4.03 0.52 N 19 20. i j 20 11 22 33 1 2 3 1 i j 3 i j 5 i j 7 i j 9 i j ija 21. A1~A4 A1A2 7 21 A1 9 7 5 3 1 3 5 7 9 A2 9 7 5 3 1 3 5 7 9 A3 9 7 5 3 1 3 5 7 9 A4 A2 9 7 5 3 1 3 5 7 9 A3 9 7 5 3 1 3 5 7 9 A4 A3 9 7 5 3 1 3 5 7 9 A5 A: A1: A2: A3: A4: B: B1: B2: B1: 22. 10~15 22 1 2 3 4 23. 23 AWW WAnA (eigenvectors) (eigenvalues) AWW WAnA (eigenvectors) (eigenvalues) eigen WW =1 =-1 24. nnA 24 111 1 11 1 21 2 12 112 nn n n aa a a aa A ji ij a a 1 iiii aa 25. 25 10 02 A 0 1 W 1 0 W =? AWW 0 1 2 0 2 0)1(10 1012 0 1 10 02 AW 26. 26 51 122 )det( IA AW= W AIW IW det(A- I)W=0 232 0)2()1( )112()5()2( 2 1 2 1 1 51 122 x x x x 1,2 21 xx 2 1 2 1 2 51 122 x x x x 1,7 21 xx = -1 = -2 51 122 A 27. >3 Step1 Step2 Step3AW= W 27 A B C A 1.00 0.33 3.00 1.44 1.00 B 3.00 1.00 2.00 2.00 1.82 C 0.33 0.50 1.00 0.61 0.55 1 1/33 28. 28 A B C A 1 2 3 B 1/2 1 4 C 1/3 1/4 1 817.13213 26.1415.03 437.0125.033.03 514.3437.026.1817.1 Step1 Step2 514.3/437.0 514.3/26.1 514.3/817.1 124.0 359.0 517.0 108.3 3 113.3103.3108.3 max Step3AW= W 125.033.0 415.0 321 AW 124.0 359.0 517.0 386.0 114.1 607.1 = W 113.3 103.3 108.3 124.0/386.0 359.0/114.1 517.0/607.1 124.0 359.0 517.0 124.0 359.0 517.0 = n i i i nW AW 1 max )( 29. 29 Ai(i=1,2,,n) 0An max=n (Consistency Index, C.I.) max=n max>n AWnWAW maxW AWnWAW maxW 1 .. max n n IC n 30. Saaty(1980)500C.I. C.I. (Random Index, R.I.) (Consistency Ratio, C.R.) (Consistency Ratio of the Hierarchy, C.R.H.) 30 N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 R.I. 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.48 1.48 1.56 1.57 1.59 .. .. .. IR IC RC .).)(( .).)(( .. IR IC HRC C.R. 39 40. Expert Choice Insert Child of Current Node -> Enter Add Alternative ->OK 40 41. Expert Choice 41 Assessment->Direct 42. Expert Choice 42 C.I. 43. Expert Choice 43 44. Expert Choice 44 45. Expert Choice Participants -> Edit -> Add N Participants -> 45 46. Expert Choice N Assessment -> Combine Participants Judgments/Data -> Entire Hierarchy 46 47. Expert Choice BothN 47 48. Expert Choice Synthesize -> With Respect to Goal Overall InconsistencyB>CA>C AB3 BC2A B6 7. 8. 54 55. ANP 55 ( )() 56. 56 ? 57. 57 1 2 3 4 AHP 58. 58 a1 a2 ,, an A CB D b1 b2 ,, bn c1 c2 ,, cn d1 d2 ,, dn Delphi 59. 59 60. i j 60 AA A1A1 A2A2 A3A3 A A1 A2 A3 1 i j 3 i j 5 i j 7 i j 9 i j ija 61. A1 B1A2 7 61 A2 9 7 5 3 1 3 5 7 9 B1 62. () 0 62 000 00 00 0000 43 3332 2221 W WW WW W () ne e e W 1 12 11 21 63. W21W22W32W33W43 1 1 () 63 000 00 00 0000 43 3332 2221 W WW WW W 1 1 1 000 00 00 0000 43 3332 2221 W WW WW W 1 1 1 1 1 12* lim k k WW 64. 64 C.I. -> -> -> 67. Step3 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 1. 1-1. 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 1-2. 67 68. 68 2-1. 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 2-5. 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 9 7 5 3 1 3 5 7 9 1-3. 9 7 5 3 1 3 5 7 9 1-4. 9 7 5 3 1 3 5 7 9 1-5. 69. Step4 Step5 69 1 3 2 5 7 0.333 1 0.5 2 3 0.5 2 1 4 6 0.2 0.5 0.25 1 2 0.143 0.333 0.167 0.5 1 05.0 082.0 282.0 148.0 438.0 1. 1-1~1-4. 1 7 0.5 0.5 0.14 1 0.2 0.2 2 5 1 0.5 2 5 2 1 42.0 297.0 054.0 228.0 25.0 75.0 1 3 0.33 1 2.0 8.0 1 4 0.25 1 75.0 25.0 1 0.33 3 1 333.0 667.0 1 2 0.5 1 073.0..065.0..196.4max RCIC 009.0..010.0..039.5max RCIC 0..0..2max RCIC 0..0..2max RCIC 0..0..2max RCIC 0..0..2max RCIC 70. 70 1 2 3 0.5 1 2 0.333 0.5 1 1 2 2 0.5 1 1 0.5 1 1 1 1 0.333 1 1 0.333 3 3 1 1 2 0.5 0.5 1 0.25 2 4 1 163.0 297.0 54.0 25.0 25.0 5.0 6.0 2.0 2.0 571.0 143.0 286.0 1 0.333 2 3 1 6 0.5 0.167 1 111.0 667.0 222.0 2-1~2-5. 009.0..005.0..009.3max RCIC 0..0..3max RCIC 0..0..3max RCIC 0..0..3max RCIC 0..0..3max RCIC 71. 71 Goal Goal 0 0 0 0 0 0 0 0 0 0.437 0 0.750 0.800 0 0 0 0 0 0.148 0.232 0 0.200 0.250 0.667 0 0 0 0.282 0.055 0.250 0 0.750 0 0 0 0 0.082 0.417 0 0 0 0.333 0 0 0 0.050 0.296 0 0 0 0 0 0 0 0 0.540 0.222 0.500 0.200 0.286 0 0 0 0 0.297 0.667 0.250 0.200 0.143 0 0 0 0 0.163 0.111 0.250 0.600 0.571 0 0 0 Goal Goal 0 0 0 0 0 0 0 0 0 0.437 0 0.375 0.400 0 0 0 0 0 0.148 0.116 0 0.1 0.125 0.333 0 0 0 0.282 0.027 0.125 0 0.375 0 0 0 0 0.082 0.208 0 0 0 0.167 0 0 0 0.050 0.148 0 0 0 0 0 0 0 0 0.270 0.111 0.250 0.100 0.143 0 0 0 0 0.148 0.333 0.125 0.100 0.071 0 0 0 0 0.082 0.056 0.125 0.300 0.286 0 0 0 0 0 000 32 2221 W WWW Goal Goal 0 0 0 0 0 0 0 0 0 0.161 0.161 0.161 0.161 0.161 0.161 0 0 0 0.110 0.110 0.110 0.110 0.110 0.110 0 0 0 0.099 0.099 0.099 0.099 0.099 0.099 0 0 0 0.083 0.083 0.083 0.083 0.083 0.083 0 0 0 0.048 0.048 0.048 0.048 0.048 0.048 0 0 0 0.191 0.191 0.191 0.191 0.191 0.191 0 0 0 0.169 0.169 0.169 0.169 0.169 0.169 0 0 0 0.140 0.140 0.140 0.140 0.140 0.140 0 0 0 1 1 1 1 1 1 72. 72 0.161 0.322 0.110 0.219 0.099 0.197 0.083 0.166 0.048 0.095 0.191 0.382 0.169 0.338 0.140 0.280 Goal 0.161 0.161 0.161 0.161 0.161 0.161 0.110 0.110 0.110 0.110 0.110 0.110 0.099 0.099 0.099 0.099 0.099 0.099 0.083 0.083 0.083 0.083 0.083 0.083 0.048 0.048 0.048 0.048 0.048 0.048 0.191 0.191 0.191 0.191 0.191 0.191 0.169 0.169 0.169 0.169 0.169 0.169 0.140 0.140 0.140 0.140 0.140 0.140 73. Super Decisions (AHP) File -> New Choose the new file name -> 73 74. Super Decisions Design -> Cluster -> New New Cluster DialogName Goal CreateAnother 74 75. Super Decisions New Cluster DialogName CriteriaAlternatives 75 76. Super Decisions Create node in cluster New Node DialogName 76 77. Super Decisions Create node in cluster New Node DialogName 1 -> Create Another -> 23 45 77 78. Super Decisions Create node in cluster New Node DialogName1 ->Create Another -> 23 78 79. Super Decisions Node connexions from Node Selector1 2345 Okay 79 80. Super Decisions 80 81. Super Decisions Node connexions from Node Selector 1-> Create Another -> 23 81 82. Super Decisions Assess/Compare -> Pairwise Comparisons Node compare interface 82 83. Super Decisions 83 84. Super Decisions 84 C.I. 85. Super Decisions 85 86. Super Decisions Computations -> Priorities 86 87. Super Decisions (ANP) Node connexions from Node Selector 87 88. Super Decisions 88 89. Super Decisions 89 90. Super Decisions 90 a1 a2 a3 A CB D b1 b2 b3 c1 c2 c3 d1 d2 d3