Dual Consensus Measure for Multi-Perspective Multi-Criteria Group Decision Making

1. Dual Consensus Measure
for Multi-Perspective Multi-
Criteria Group Decision Making
Ivan Palomares Carrascosa
Lecturer (Assistant Professor) in Data Science and AI
Decision Support and Recommender Systems (DSRS) Research Group
University of Bristol, United Kingdom
E-mail: i.palomares@bristol.ac.uk
Twitter: @ivan_uob

2. CONTENTS
•DECISION-MAKING FRAMEWORK
•MOTIVATION
•DUAL CONSENSUS MEASURE
•APPLICATION EXAMPLE
•CONCLUDING REMARKS

3. DECISION-MAKING FRAMEWORK
•MCGDM
• Alternatives: ! = #$, #&, … , #( , ) ≥ 2,
• Participants (experts): , = -$, -&, … , -. , / ≥ 2
• Criteria: 0 = 1$, 1&, … , 12 , 3 ≥ 2
• Criteria have associated importance weights
• Individual preferences à decision matrices
Location Price Condition
Apt 1 0.8 0.5 0.2
Apt 2 0.3 0.7 0.5
Apt 3 0.55 0.25 0.7
Apt 4 0.5 0.5 0.6
DECISION MATRIX IN [0,1]
INTERVAL

4. MOTIVATION
• Most MCGDM problems assume a common setting of the
relative importance of criteria for the whole group, BUT…
• In many real problems, different participants have different
perspectives about the relative importance of such criteria.

5. MOTIVATION
• Consensus building processes
• Introduced in GDM problems and their extensions to find highly accepted
solutions
• Consensus measures
• Currently not suitable to measure
agreement level in multi-perspective
decision groups

6. DUAL CONSENSUS MEASURE
• Captures level of agreement among participants on:
1. Global satisfaction on each alternative
2. Partial satisfaction on each alternative under each criterion
3. Similarity between perspectives of participants (weighted given to criteria)

7. DUAL CONSENSUS MEASURE
1. Global satisfaction on each alternative
• Distance based on global alternative performance
• Calculated for each alternative and pair of experts
W1 = [.4 .2 .4]T W2 = [.2 .4 .4]T
P1(x1) = 0·0.4+0.75·0.2+1·0.4 = 0.55
P2(x1) = 0.75·0.2+1·0.4+0·0.4 = 0.55
dG(p1, p12) = |0.55 − 0.55| = 0

8. DUAL CONSENSUS MEASURE
2. Partial satisfactions on each alternative
• Distance based on alternative performances per criterion,
and individual perspectives on criteria weights
• Calculated for each alternative and pair of experts
W1 = [.4 .2 .4]T W2 = [.2 .4 .4]T dP (p1 , p12 ) = (0.794 + 0.330 + 1)/3 = 0.708

9. DUAL CONSENSUS MEASURE
3. Putting it all together
• Consensus degree between two experts <i, i’> on an alternative xj
a = 1 à only global performance is taken into account
a = 0.5 à global and partial performances are equally considered

10. DUAL CONSENSUS MEASURE
3. Putting it all together

11. APPLICATION EXAMPLE – LOGISTICS SECURITY
•Hazardous material transportation
• 4 candidate routes (alternatives), 3 criteria (efficiency, population density, road
condition), 6 experts on secure logistics
(i) increasing the relative importance of dG
wrt dP (by increasing α), the dual
consensus measure behaves more
optimistically
(ii) Considering distances between partial
performances of alternatives à stronger
sensitivity towards disagreement positions
(iii) the highest (resp. lowest) variability
in the consensus degrees as α increases are
observed for x1 (resp. x3).

12. CONCLUDING REMARKS
• First characterization of consensus measure for multi-perspective
MCGDM
• Individual perspectives on the relative importance of criteria are
integrated in the measure of agreement among preferences
• FUTURE WORK:
• Generalize to MCGDM frameworks with different preference formats
• define a complete consensus model based on proposed measure
• Large-group decision making application (diversity, non-cooperative
behaviors…)

13. COMING NOVEMBER 2018!
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