Norihiro Saikawa Department of Computer and Information Science Hosei University

1. Constructing the PAHP-based Decision Support System by Considering the Ambiguity in Decision Making Norihiro Saikawa Department of Computer and Information Science Hosei University 3-7-2 Kajino-cho, 184-8584, Japan

2. Outline Outline • Introduction to AHP • A Problem in AHP • Solving the problem by PAHP • Comparing the performance between AHP and PAHP • Conclusions & future work Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 2/16

3. Introduction to AHP (1/3) All the criteria have to be compared with each other one by one to calculate the importance of each criterion Introduction to AHP AHP = Analytic Hierarchy Process Goal Criterion Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 3/16

4. Introduction to AHP (2/3) Safety is Equally preferred to safety These values have to be less than 0.1 The reciprocal value of 3.0 = 1/3 is given to the cell Safety is slightly more preferred to appearance How to obtain the importance Pairwise comparison Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 4/16

5. Intensity of preference Definition Introduction to AHP (3/3) 1 A is equallypreferred to B If activity i has one of the above non-zero numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i 3 A is slightly more preferred to B 5 A is strongly more preferred to B 7 A is very strongly more preferred to B 9 A is extremelymore preferred to B 2,4,6,8 Intermediate intensity Reciprocals of above non-zero The ratio scale of preference (Saaty) A (column) is compared to B (row) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 5/16

6. A problem in AHP (1/2) Set of the scale of AHP (integer) Measurement error using scale These errors have possibilities to change the rank of the criterion User’s true preference = P (real number) (difficult to identify or unknown for the user) A problem in AHP 1 n n-1 ・・・ ・・・ 9 P Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 6/16

7. Solving the problem by PAHP (1/6) Measurement error using scale Set of the scale of PAHP (decimal) PAHP makes the measurement error smaller Solving the problem by PAHP 1 n n-1 ・・・ ・・・ 9 P X1 X2 Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 7/16

8. Solving the problem by PAHP (2/6) PAHP Make a problem hierarchy Input the degree of confidence about solving the problem Do pairwise comparison Estimate user’s ambiguity in making decision No C.I < 0.1 ∧ C.R. < 0.1 Yes The importance of each criterion is calculated Difference of the process AHP Make a problem hierarchy Do pairwise comparison C.I < 0.1 ∧C.R. < 0.1 No Yes The importance of each criterion is calculated Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 8/16

9. Solving the problem by PAHP (3/6) +8 +8 +1 B is extremely preferred to A A is equally preferred to B A is extremely preferred to B Concept of response value (R) Correspondence of the ratio scale of preference and the response value Ratio scale of preference by Saaty A (column ) B (row) Response value (R) A screen shot of how to apply ratio scale of preference Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 9/16

10. Solving the problem by PAHP (4/6) DC -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 How to input user’s degree of confidence 17 kinds of verbal expressions to measure the degree of confidence Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 10/16

11. Solving the problem by PAHP (5/6) S x L U R How to estimate the ambiguity Ｘ L: The lower limit of the user’s true preference U: The upper limit of the user’s true preference Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 11/16

12. The adjustment coefficient (C) The degree of confidence Solving the problem by PAHP (6/6) 1 －8 0.5 －4 0 0 Estimated user’s preference using PAHP －0.5 4 R+1 －1 8 Estimated user’s preference using PAHP R+1 How to estimate user’s true preference Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 12/16

13. Comparing the performance between AHP and PAHP (1/3) Comparing the performance between AHP and PAHP (1/3) • We simulated the process of pairwise comparison　 　in 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. Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 13/16

14. Comparing the performance between AHP and PAHP (2/3) Less consistent Extremely not confident (scale1) Not sure (=AHP) Extremely Confident (scale17) More consistent Comparing the performance between AHP and PAHP (2/3) Comparison in terms of consistency Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 14/16

15. Comparing the performance between AHP and PAHP (3/3) Extremely confident Not sure (=AHP) Extremely not confident Comparing the performance between AHP and PAHP (3/3) Comparison in terms of stability Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making 15/16

16. Conclusions & future work Conclusions & future work The advantage of using PAHP: • Being able to estimate the preference of the user more precisely than AHP Necessary improvement of PAHP: • 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 16/16