Constructing the PAHP-based Decision Support System by Considering the Ambiguity in Decision MakingNorihiro SaikawaDepartment of Computer and Information ScienceHosei University3-7-2 Kajino-cho, 184-8584, Japan

Outline Introduction to AHP

A Problem in AHP

Solving the problem by PAHP

Comparing the performance between AHP and PAHP

Conclusions & future work

Outline Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making2/16

Introduction to AHP AHP = Analytic Hierarchy ProcessConstructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making3/16Introduction to AHP (1/3) GoalCriterion

How to obtain the importance 4/16Pairwise comparisonIntroduction to AHP (2/3) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making

The ratio scale of preference (Saaty)5/16Introduction to AHP (3/3) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision MakingA (column) is compared to B (row)

A problem in AHP6/16A problem in AHP (1/2) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Makingn-1nP19

Solving the problem by PAHP7/16Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision MakingX1X2n-1nP19Solving the problem by PAHP (1/6)

Difference of the process8/16Solving the problem by PAHP (2/6) Make a problem hierarchyDo pairwise comparisonThe importance of each criterion is calculated C.I < 0.1 C.R. < 0.1YesNoAHPConstructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making

Concept of response value (R)9/16Solving the problem by PAHP (3/6) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision MakingRatio scale of preference by SaatyResponse value (R)A (column )B (row)Correspondence of the ratio scaleof preference and the response valueA screen shot of how to apply ratio scale of preference

How to input users degree of confidenceConstructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making10/16Solving the problem by PAHP (4/6) 17 kinds of verbal expressions to measure the degree of confidence

How to estimate the ambiguity11/16Solving the problem by PAHP (5/6) L: The lower limit of the users true preferenceU: The upper limit of the users true preferenceConstructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making

How to estimate users true preference12/16Solving the problem by PAHP (6/6) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making

Comparing the performance between AHP and PAHP (1/3)13/16 We simulated the process of pairwise comparisonin the AHP and PAHP and compared the performance with each other in terms of consistency and stability.

As a result, we found that the PAHP outperforms the AHP when the user is confident about solving the confronting problem. Comparing the performance between AHP and PAHP (1/3)Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making

Comparing the performance between AHP and PAHP (2/3)14/16Comparison in terms of consistencyComparing the performance between AHP and PAHP (2/3)Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making

Comparing the performance between AHP and PAHP (3/3)Comparison in terms of stability15/16Comparing the performance between AHP and PAHP (3/3)Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making

Graph2

93.2592592593

92.7037037037

93.1111111111

92.6666666667

91.7777777778

91.6296296296

91.1111111111

90.7777777778

90.0740740741

89.8148148148

89.6296296296

88.5555555556

88.3333333333

88.0740740741

87.7407407407

87.037037037

86.962962963

The index of the scale

Average total failure raet of preference

The average total failure rates of different scales (%)

Sheet1

scale1scale2scale3scale4scale5scale6scale7scale8scale9scale10scale11scale12scale13scale14scale15scale16scale17

5147535446494748444346454340423735

6361635858625760555555535151504850

7169727068636465636259596361605655

8378798076757473727374686566696366

8684868381817978777775737371687172

8990908886838580838383767980778077

9293909189919188868582828483828178

9595959494919191909090868887858284

9696969793939393939093908687918686

9797989797969594929494919190888989

9899989798989796939594959292929291

9998989998989797969396959693949394

9999999999989797979896959596959594

10099999999999898999898969697959697

10099999999999999989897989798979697

1001001009999999998999997979797979798

100100999999999999999898999898979897

100100100100991009999999999989898989999

100100100100100100100100999999999998989898

99991009910010099100999999999999999999

100100100100100100100100999999999999999998

10010010010010010010010010010010010099100999999

1001001001001001001009910099991009999999999

10010010010010010010010010099999999999910099

10010010010010010010010010010010099100991009999

10010010010010010010099100100100100991001009999

10010010010010010010010010010099100100100999999

93.259259259392.703703703793.111111111192.666666666791.777777777891.629629629691.111111111190.777777777890.074074074189.814814814889.629629629688.555555555688.333333333388.074074074187.740740740787.03703703786.962962963

Sheet1

5147535446494748444346454340423735

6361635858625760555555535151504850

7169727068636465636259596361605655

8378798076757473727374686566696366

8684868381817978777775737371687172

8990908886838580838383767980778077

9293909189919188868582828483828178

9595959494919191909090868887858284

9696969793939393939093908687918686

9797989797969594929494919190888989

9899989798989796939594959292929291

9998989998989797969396959693949394

9999999999989797979896959596959594

10099999999999898999898969697959697

10099999999999999989897989798979697

1001001009999999998999997979797979798

100100999999999999999898999898979897

100100100100991009999999999989898989999

100100100100100100100100999999999998989898

99991009910010099100999999999999999999

100100100100100100100100999999999999999998

10010010010010010010010010010010010099100999999

1001001001001001001009910099991009999999999

10010010010010010010010010099999999999910099

10010010010010010010010010010010099100991009999

10010010010010010010099100100100100991001009999

10010010010010010010010010010099100100100999999

scale1

scale2

scale3

scale4

scale5

scale6

scale7

scale8

scale9

scale10

scale11

scale12

scale13

scale14

scale15

scale16

scale17

Sheet2

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

The index of the scale

Average total failure of preference

The average total failure of each scales

Sheet3

MBD0006E88C.xls

Graph2

5147535446494748444346454340423735

6361635858625760555555535151504850

7169727068636465636259596361605655

8378798076757473727374686566696366

8684868381817978777775737371687172

8990908886838580838383767980778077

9293909189919188868582828483828178

9595959494919191909090868887858284

9696969793939393939093908687918686

9797989797969594929494919190888989

9899989798989796939594959292929291

9998989998989797969396959693949394

9999999999989797979896959596959594

10099999999999898999898969697959697

10099999999999999989897989798979697

1001001009999999998999997979797979798

100100999999999999999898999898979897

100100100100991009999999999989898989999

100100100100100100100100999999999998989898

99991009910010099100999999999999999999

100100100100100100100100999999999999999998

10010010010010010010010010010010010099100999999

1001001001001001001009910099991009999999999

10010010010010010010010010099999999999910099

10010010010010010010010010010010099100991009999

10010010010010010010099100100100100991001009999

10010010010010010010010010010099100100100999999

scale1

scale2

scale3

scale4

scale5

scale6

scale7

scale8

scale9

scale10

scale11

scale12

scale13

scale14

scale15

scale16

scale17

The number of criterion

Total failure rate

Total failure rates for different scales

Sheet1

scale1scale2scale3scale4scale5scale6scale7scale8scale9scale10scale11scale12scale13scale14scale15scale16scale17

5147535446494748444346454340423735

6361635858625760555555535151504850

7169727068636465636259596361605655

8378798076757473727374686566696366

8684868381817978777775737371687172

8990908886838580838383767980778077

9293909189919188868582828483828178

9595959494919191909090868887858284

9696969793939393939093908687918686

9797989797969594929494919190888989

9899989798989796939594959292929291

9998989998989797969396959693949394

9999999999989797979896959596959594

10099999999999898999898969697959697

10099999999999999989897989798979697

1001001009999999998999997979797979798

100100999999999999999898999898979897

100100100100991009999999999989898989999

100100100100100100100100999999999998989898

99991009910010099100999999999999999999

100100100100100100100100999999999999999998

10010010010010010010010010010010010099100999999

1001001001001001001009910099991009999999999

10010010010010010010010010099999999999910099

10010010010010010010010010010010099100991009999

10010010010010010010099100100100100991001009999

10010010010010010010010010010099100100100999999

Sheet1

scale1

scale2

scale3

scale4

scale5

scale6

scale7

scale8

scale9

scale10

scale11

scale12

scale13

scale14

scale15

scale16

scale17

Sheet2

Sheet3

Graph2

5147535446494748444346454340423735

6361635858625760555555535151504850

7169727068636465636259596361605655

8378798076757473727374686566696366

8684868381817978777775737371687172

8990908886838580838383767980778077

9293909189919188868582828483828178

9595959494919191909090868887858284

9696969793939393939093908687918686

9797989797969594929494919190888989

9899989798989796939594959292929291

9998989998989797969396959693949394

9999999999989797979896959596959594

10099999999999898999898969697959697

10099999999999999989897989798979697

1001001009999999998999997979797979798

100100999999999999999898999898979897

100100100100991009999999999989898989999

100100100100100100100100999999999998989898

99991009910010099100999999999999999999

100100100100100100100100999999999999999998

10010010010010010010010010010010010099100999999

1001001001001001001009910099991009999999999

10010010010010010010010010099999999999910099

10010010010010010010010010010010099100991009999

10010010010010010010099100100100100991001009999

10010010010010010010010010010099100100100999999

scale1

scale2

scale3

scale4

scale5

scale6

scale7

scale8

scale9

scale10

scale11

scale12

scale13

scale14

scale15

scale16

scale17

The number of criterion

Total failure rate

Total failure rates of different scales (%)

Sheet1

scale1scale2scale3scale4scale5scale6scale7scale8scale9scale10scale11scale12scale13scale14scale15scale16scale17

5147535446494748444346454340423735

6361635858625760555555535151504850

7169727068636465636259596361605655

8378798076757473727374686566696366

8684868381817978777775737371687172

8990908886838580838383767980778077

9293909189919188868582828483828178

9595959494919191909090868887858284

9696969793939393939093908687918686

9797989797969594929494919190888989

9899989798989796939594959292929291

9998989998989797969396959693949394

9999999999989797979896959596959594

10099999999999898999898969697959697

10099999999999999989897989798979697

1001001009999999998999997979797979798

100100999999999999999898999898979897

100100100100991009999999999989898989999

100100100100100100100100999999999998989898

99991009910010099100999999999999999999

100100100100100100100100999999999999999998

10010010010010010010010010010010010099100999999

1001001001001001001009910099991009999999999

10010010010010010010010010099999999999910099

10010010010010010010010010010010099100991009999

10010010010010010010099100100100100991001009999

10010010010010010010010010010099100100100999999

Sheet1

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

00000000000000000

scale1

scale2

scale3

scale4

scale5

scale6

scale7

scale8

scale9

scale10

scale11

scale12

scale13

scale14

scale15

scale16

scale17

Sheet2

Sheet3

Conclusions & future workConclusions & future work16/16The advantage of using PAHP:

Necessary improvement of PAHP:

Being able to estimate the preference of the user more precisely than AHP To apply the decision time of the user in the process of pairwise comparison to estimate the confidence more precisely.Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making