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