Constructing the PAHP-based Decision Support System by Considering the Ambiguity in Decision Making Norihiro Saikawa Department of Computer and Information Science Hosei University Kajino-cho, , 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

Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making3/16 Introduction to AHP (1/3) AHP = Analytic Hierarchy Process Introduction to AHP All the criteria have to be compared with each other one by one to calculate the importance of each criterion Goal Criterion

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

5/16 The ratio scale of preference (Saaty) Introduction to AHP (3/3) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making A (column) is compared to B (row) Intensity of preferenceDefinition 1A is equally preferred to B 3A is slightly more preferred to B 5A is strongly more preferred to B 7A is very strongly more preferred to B 9A is extremely more preferred to B 2,4,6,8Intermediate intensity Reciprocals of above non-zero 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

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

Solving the problem by PAHP 7/16 Set of the scale of PAHP (decimal) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making X1X2 n-1 n P Measurement error using scale 1 ・・・ 9 PAHP makes the measurement error smaller Solving the problem by PAHP (1/6)

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

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

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

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

12/16 Solving the problem by PAHP (6/6) How to estimate user’s true preference The adjustment coefficient (C) The degree of confidence 1 －8－8 0.5 －4－4 00 － －1－1 8 R+1 Estimated user’s preference using PAHP R+1 Estimated user’s preference using PAHP 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 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. 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) 14/16 Comparison in terms of consistency Comparing the performance between AHP and PAHP (2/3) Constructing the PAHP-based Decision Support System Considering the Ambiguity in Decision Making More consistent Less consistent Extremely not confident (scale1) Not sure (=AHP) Extremely Confident (scale17)

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

Conclusions & future work 16/16 The 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