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AHP
3.1 AHP
analytic hierarchy processAHP
Thomas,L.Saaty 1971
uncertainty
1972
1972 7 Saaty
no peace, no war
1973 Saaty AHP
1974 1978
1980
Saaty
84
Saaty1980AHP 12
Decision-making Problem
1.Setting Priorities
2.Generating a Set of Alternative
3.Choosing a Best Policy Alternative
4.Determining Requirements
5.Allocating Resources
6.Predicting Outcomes and Risk Assessment
7.Measuring Performance
8.Designing Systems
9.Ensuring System Stability
10.Optimizing
11.Planning
12.Conflict Resolution
24
AHPmulti-object
pairwise comparison matrix
eigen value
77
AHP
AHP
AHP
78
AHP
AHP
AHP
25
3.2 AHP
AHP
AHP 9
1.classescomponents
2.independence
3.
4.ratio scale
5. pairwise comparison
(positivereciprocal matrix)
6.transitivityA
BB C A C
A BB C A C
7.
consistency
8.weighting principle
9.
1989
26
3.3 AHP
1.
(brain storming)(interpretive structural modelling, ISM)
(hierarchical structural analysis,HSA)
(group method of structural modelling,GMSM) PATTERN
(planning assistance through technical evaluation of relevance numbers)
(eigenvector method,EM)(least squares
method,LSM)(geometric means method,GMM)Churchman
Scheffe AHP
2.
1focus
2
3 Satty
4
27
5
6
3.
2
1complete hierarch e e + 1
2incomplete hierarchy f f1
4.Saaty
1
2
3
4
28
3.4 AHP
AHP
AHP
(Ratio
Scale)
13579 246
8 AHP 3.1
3.1 AHP
,,,
Saaty ,T.L.,1980The Analytic Hierarchy ProcessMcGraw Hill,Inc.,New
York.
29
3.5 AHP
AHP 7
1.
2.
delphi methodbrainstorming method
3.
7
7 n/7
4.
1 9()
5.
30
A 1
12 1 12 1
21 2 21 2
1 2 1 2
1 11 1/ 1
1 1/ 1/ 1
n n
n n
n n n n
a a a aa a a
a a a a
=
L L
L L
L L L L L L L L
L L
a
n
a
2
1 1 1 2 1
2 1 2 2 2
1 2
/ / // / /
/ / /
n
n
n n n
w w w w w ww w w w w w
w w w w w w
L
L
L L L L
L
n A
1
1/ji ija =
i i-1
/ij i ja w w=
1 2, , nw w wK
6.
eigen value
eigen vector Wpriority vector
1
Saaty1982
1
1
1 1
n n
ijj
i nn
iji j
aw
a
=
= =
=
, 1, 2, ...i j n= K 3
2 max
A w w =uv uv uuv
( A w
31
) w
1 112 1
21 2 2
1 2 4 4
11/ 1
1/ 1/ 1
n
n
n n
w wa aa a w w
a a w w
=
L
L
L L L L L L
L
2
4
m a x
1 2max1 2
1 ...... nn
ww wn w w w
= + + +
5
7.
consistency ratio,CR
consistency ratio hierarchy,CRH Saaty
0.1
1consistency index, C.I.
max. .1
nC In
=
6
2consistency ratio, C.R.
. .. .
. .C IC RR I
= 7
random indexR.I. 1 9
3.2
32
3.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
R.I. 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 1.51 1.48 1.56 1.57 1.58
Saaty ,T.L.,1980The Analytic Hierarchy ProcessMcGraw Hill,Inc.,New York.
3consistency ratio hierarchy, C.R.H
(consistency
index of the hierarchy, C.I.H.) (random index of
the hierarchy, R.I.H.)
. . .C I H = ( C.I.) 8
. . .R I H = () ( R.I.) 9
. . .. . .
. . .C I HC R HR I H
= 10
C.R.H.< 0.1
AHP 3.1
33
C.I. C.R. 0.1
3.1 AHP
Thomas L. Saaty,1980,The Analytic Hierarchy Process. McGraw-Hill, New
York, pp.105
34
3.6 Expert Choice
Expert ChoiceAHP
hierarchical structure
Expert Choice
Expert Choice 2000.
http://www.expertchoice.com
Expert Choice pairwiseExpert
Choice
"what-if"
Expert Choice
InternetExpert Choice
Group
InternetInternet
Expert Choice keypad
keypads 150
Internet Keypad
Expert Choice Group
35
Expert Choice Group
Expert Choice
1.
2.ModelView TreeView ClusterView
Information Documents
3.Tree View
1 objectives
2 TreeView ClusterView
3 Hierarchy
4.Information Documents
5.Notes
6.Data Grid Approaches
1 Utility Curves
2Step Function
3Ratings
4Direct Entry of Priorities
7. Data Conversion
8. Printing/ReportingMicrosoft Word Excel
http://www.ixon.com.tw/
Expert Choice AHP
(sensivitive)
(likelihood)(Assignment)
36
1.Performance
2.Dynamic
3.Gradient
4.Head-to-head
5.Two dimensional
92
Expert Choice
93
1.
1
2
3
2. 5
3.
1 3.2
3.2 Expert Choice
37
2 3.3
3.3 Expert Choice
38
35 3.4
3.4 Expert Choice 5
4 3.5
3.5 Expert Choice
39
5 3.6
3.6 Expert Choice
6 3.7
3.7 Expert Choice
40
7Expert Choice 94
Performance
3.8
3.8 Expert Choice Performance
Dynamic
3.9
3.9 Expert Choice Dynamic
41
Gradient3.10
3.10 Expert Choice Gradient
Head-to-head
3.11
3.11 Expert Choice
Head-to-head
42
Two dimensionalXY(X,Y)3.12
3.12 Expert Choice
Two dimensional
AHP
Ossadnik and Lange(1999)
AHP-based evaluation of AHP-Software
AHPAuto Man
Expert ChoiceHIPRE 12
AHP
AHP Expert
Choice AutoMan HIPREExpert Choice
Ossadnik and Lange1999
43
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