PROMETHEE-compatible presentations of multicriteria evaluation tables
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- Alannah Barber
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1 PROMETHEE-compatible presentations of multicriteria evaluation tables Karim Lidouh, Anh Vu Doan*, Yves De Smet CoDE-SMG, Université libre de Bruxelles 2nd International MCDA Workshop on PROMETHEE: Research and Case Studies 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 1
2 Is it better to order a table like this...? Best cities ranking subset - Evaluation table Perm City Stability Healthcare Culture and Education Infrastructure Spatial Environment Characteristics 1 Hong Kong Stockholm Rome New York Atlanta Buenos Aires Santiago Sao Paulo Mexico City New Delhi Istanbul Jakarta Tehran Dakar nd International MCDA Workshop on PROMETHEE:Research and Case Studies 2
3 ... or like this...? Best cities ranking subset - Evaluation table Perm City Infrastructure Education Stability Culture and Healthcare Spatial Environment Characteristics 5 Atlanta Buenos Aires Dakar Hong Kong Istanbul Jakarta Mexico City New Delhi New York Rome Santiago Sao Paulo Stockholm Tehran nd International MCDA Workshop on PROMETHEE:Research and Case Studies 3
4 ... or with some colors and smart reordering? Crit4 Crit5 Crit3 Crit1 Crit6 Crit2 NetFlows A ,4 91, ,9 95,8 0, A ,4 85, ,5 0, A ,9 91, ,3 87,5 0, A ,3 91, ,2 91,7 0, A ,9 91, ,9 91,7 0, A ,7 85, ,3 87,5 0, A7 83,3 85,7 89, ,1 70,8-0,03846 A8 66,7 66,1 80, ,4 70,8-0,14615 A ,4 82, ,8 66,7-0,17885 A ,9 55, ,6 58,3-0,30865 A11 58,3 67,9 68, ,5 50-0,35481 A ,9 35, ,6 62,5-0,575 A12 66,7 57,1 59, ,3 45,8-0,65577 A ,5 59, ,6 41,7-0, nd International MCDA Workshop on PROMETHEE:Research and Case Studies 4
5 We can use PROMETHEE-GAIA to enrich evaluation tables with multicriteria information Analyse visuelle globale Delta: 90.30% Dakar Santiago Buenos Aires Atlanta Jakarta Istanbul Sao Paulo Culture Stability Infrastructure and Environment Healthcare Education Stockholm Tehran New Delhi New York Rome Hong Kong Mexico City Spatial Characteristics GAIA plane for the best cities subset 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 5
6 We can order alternatives and criteria on basis of netflows, weights, angle and proximity found in GAIA Possibilities for the alternatives: Netflow Angle Proximity Possibilities for the criteria: Weights Angle Proximity 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 6
7 We can use PROMETHEE-GAIA to enrich evaluation tables with multicriteria information Analyse visuelle globale Delta: 90.30% Dakar Santiago Buenos Aires Atlanta Jakarta Istanbul Sao Paulo Culture Stability Infrastructure and Environment Healthcare Education Stockholm Tehran New Delhi New York Rome Hong Kong Mexico City Spatial Characteristics GAIA plane for the best cities subset 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 7
8 4 combinations of orders are actually interesting Combinations of orders and chosen representations Order of criteria Weights Angle Proximity Order Netflows of Angle alternatives Proximity 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 8
9 The Netflow-Angle view can group all the good and bad alternatives Crit4 Crit5 Crit3 Crit1 Crit6 Crit2 NetFlows A ,4 91, ,9 95,8 0, A ,4 85, ,5 0, A ,9 91, ,3 87,5 0, A ,3 91, ,2 91,7 0, A ,9 91, ,9 91,7 0, A ,7 85, ,3 87,5 0, A7 83,3 85,7 89, ,1 70,8-0,03846 A8 66,7 66,1 80, ,4 70,8-0,14615 A ,4 82, ,8 66,7-0,17885 A ,9 55, ,6 58,3-0,30865 A11 58,3 67,9 68, ,5 50-0,35481 A ,9 35, ,6 62,5-0,575 A12 66,7 57,1 59, ,3 45,8-0,65577 A ,5 59, ,6 41,7-0,82692 Best cities subset - Netflow-Angle 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 9
10 The Netflow-Weight view can highlight characteristics that may have greater impact on the decision Crit6 Crit1 Crit3 Crit2 Crit5 Crit4 NetFlows A2 58, ,2 95,8 96, , A ,9 87,5 96, , A3 67, ,7 87,5 92, , A4 65, ,7 91,7 89, , A5 42, ,7 91,7 92, , A6 42, ,9 87,5 85, , A7 35, ,1 70,8 85,7 83,3-0,03846 A8 52, ,3 70,8 66,1 66,7-0,14615 A9 65, ,4 66,7 46,4 75-0,17885 A10 58, ,6 58,3 58,9 75-0,30865 A11 47, , ,9 58,3-0,35481 A13 53, ,9 62,5 33,9 50-0,575 A12 42, ,3 45,8 57,1 66,7-0,65577 A14 22, ,7 41,7 37,5 50-0,82692 Best cities subset - Netflow-Weight 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 10
11 The Angle-Angle view can show profiles, from the best to the worst to the best Crit4 Crit5 Crit3 Crit1 Crit6 Crit2 NetFlows A ,4 91, ,9 95,8 0, A ,9 91, ,9 91,7 0, A ,7 85, ,3 87,5 0, A7 83,3 85,7 89, ,1 70,8-0,03846 A ,5 59, ,6 41,7-0,82692 A12 66,7 57,1 59, ,3 45,8-0,65577 A11 58,3 67,9 68, ,5 50-0,35481 A8 66,7 66,1 80, ,4 70,8-0,14615 A ,9 35, ,6 62,5-0,575 A ,9 55, ,6 58,3-0,30865 A ,4 82, ,8 66,7-0,17885 A ,4 85, ,5 0, A ,9 91, ,3 87,5 0, A ,3 91, ,2 91,7 0, Best cities subset - Angle-Angle 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 11
12 The Proximity-Proximity view can group the highest values Crit2 Crit4 Crit5 Crit3 Crit1 Crit6 NetFlows A4 91, ,3 91, ,2 0, A3 87, ,9 91, ,3 0, A1 87, ,4 85, , A2 95, ,4 91, ,9 0, A5 91, ,9 91, ,9 0, A6 87, ,7 85, ,3 0, A7 70,8 83,3 85,7 89, ,1-0,03846 A9 66, ,4 82, ,8-0,17885 A10 58, ,9 55, ,6-0,30865 A13 62, ,9 35, ,6-0,575 A8 70,8 66,7 66,1 80, ,4-0,14615 A ,3 67,9 68, ,5-0,35481 A12 45,8 66,7 57,1 59, ,3-0,65577 A14 41, ,5 59, ,6-0,82692 Best cities subset - Proximity-Proximity 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 12
13 How to evaluate different representations? Developing an optimization indicator: the -indicator is the number of ordered pairs for each row and column: where n m = i + j i=1 j=1 i is the value of the i-th row: i = m m k=1 l=k+1 j is the value of the j-th column: j = n n k=1 l=k+1 1 k<l 1 fk (a i ) f l (a i ) 1 k<l 1 fj (a k ) f j (a l ) 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 13
14 How to evaluate different representations? Developing an optimization indicator: the -indicator is the number of ordered pairs for each row and column Best cities ranking subset - Evaluation table - -indicator computation City Stability Healthcare Culture and Education Infrastructure Spatial i Environment Characteristics Hong Kong Stockholm Rome New York Atlanta Buenos Aires Santiago Sao Paulo Mexico City New Delhi Istanbul Jakarta Tehran Dakar j = 593 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 14
15 Best tables found with a classical genetic algorithm Crit4 Crit3 Crit5 Crit2 Crit1 Crit6 Netflows 0, A ,2 96,4 95, ,9 A ,9 96,4 87, , A ,7 92,9 91, ,9 0, A ,7 92,9 87, ,3 0, A ,7 89,3 91, ,2 0, A ,9 85,7 87, ,3 0, A7 83,3 89,1 85,7 70, ,1-0,03846 A8 66,7 80,3 66,1 70, ,4-0,14615 A ,4 46,4 66, ,8-0,17885 A ,6 58,9 58, ,6-0,30865 A11 58,3 68,8 67, ,5-0,35481 A12 66,7 59,3 57,1 45, ,3-0,65577 A ,9 33,9 62, ,6-0,575 A ,7 37,5 41, ,6-0,82692 (a) Best found table Crit4 Crit5 Crit3 Crit1 Crit6 Crit2 NetFlows 0, A ,4 91, ,9 95,8 A ,4 85, ,5 0, A ,9 91, ,3 87,5 0, A ,3 91, ,2 91,7 0, A ,9 91, ,9 91,7 0, A ,7 85, ,3 87,5 0, A7 83,3 85,7 89, ,1 70,8-0,03846 A8 66,7 66,1 80, ,4 70,8-0,14615 A ,4 82, ,8 66,7-0,17885 A ,9 55, ,6 58,3-0,30865 A11 58,3 67,9 68, ,5 50-0,35481 A ,9 35, ,6 62,5-0,575 A12 66,7 57,1 59, ,3 45,8-0,65577 A ,5 59, ,6 41,7-0,82692 (b) Netflow-Angle Best cities subset 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 15
16 How to compare the representations? Defining a ratio R based on the -indicator Defined to keep the comparisons as objective as possible, independently of the table size R = worst best worst where best is the best found with our genetic algorithm and worst is the value associated to the worst feasible table 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 16
17 Case study 1: best cities ranking Analyse visuelle globale Delta: 88.46% Dalian Tianjin Singapore Miami Bucharest Santiago Atlanta Phnom Lusaka Penh KievKuala Lumpur WarsawStability Budapest Guangzhou Lisbon Toronto Dakar Belgrade Infrastructure Buenos Aires Boston Lagos HarareHo Chi Tashkent Shanghai Shenzhen Damascus Minh City Healthcare Chicago Stockholm Tokyo Sydney Dhaka Abidjan Nairobi Hanoi Casablanca Bangkok Culture Athens Beijing Education and Environment San Los Francisco Angeles Jakarta Manila Rio de JaneiroSt Petersburg Osaka Lima Washington Madrid Hong Kong Berlin MunichDC Paris Istanbul Johannesburg Seoul Cairo Mumbai Sao Paulo Moscow RomeAmsterdam Bogota New York Karachi New Delhi Spatial Characteristics London Tehran Caracas Mexico City GAIA plane for the best cities ranking 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 17
18 Best cities ranking representations Crit2 Crit5 Crit1 Crit6 Crit3 Crit4 NetFlows A , ,7 97, , A , , , A ,7 94, , A , ,7 97,2 91,7 0, A , ,3 97,2 91,7 0, A6 95,8 96, ,9 91, ,72029 A1 87,5 96, , , A , ,5 97,2 91,7 0, A , ,3 94, , A , , ,67337 A13 87,5 92, ,3 94, , A14 91,7 96, ,1 94, ,60163 A12 87,5 89, ,6 97, ,59058 A11 87,5 92, ,3 91, , A15 91,7 92, ,7 91, , A16 91,7 89, ,2 91, , A18 91,7 85, ,4 83,3 0, A17 91,7 89, ,3 94, , A20 83,3 89, ,8 85, , A19 91,7 96, ,7 91, , A21 91,7 92, ,9 91, , A22 87, ,7 76,6 83,3 0, A23 91,7 92, ,3 91, , A24 91,7 83, , A27 79,2 83, ,2 81,5 91,7 0,21721 A25 87,5 80, ,7 95,1 91,7 0, A30 66,7 85, ,5 72,2 83,3 0, A26 87,5 85, ,3 85, , A28 87,5 80, ,2 81,5 83,3 0, A29 83, ,3 83,1 75 0, A34 62,5 82, ,5 63,7 66,7 0, A36 70,8 66, ,4 80,3 66,7-0,00598 A35 66, ,3 81,7 91,7-0,00906 A32 70,8 82, ,3 75-0,01866 A31 70,8 85, ,1 89,1 83,3-0,02083 A41 66,7 46, ,8 82,4 75-0,04094 A33 62, , ,04783 A38 66,7 82, ,7 65,3 66,7-0,12373 A37 62,5 76, ,6 67,8 91,7-0,13696 A42 66,7 71, ,5 83,3-0,14855 A40 58,3 69, ,9 90,5 83,3-0,17174 A39 62,5 76, ,9 61,1 66,7-0,17283 A46 58,3 58, ,6 55,6 75-0,19529 A43 66,7 66, ,7 74,3 66,7-0,22572 A50 62,5 64, ,6 75,2 66,7-0,22681 A54 41,7 60, ,1 76,6 75-0,28043 A , ,1 75-0,28696 A47 62, ,7-0,29275 A52 54,2 51, ,1 56,3 66,7-0,29891 A48 58,3 64, ,1 63,2 66,7-0,3 A , ,5 68,8 58,3-0,30036 A ,3 73,4 83,3-0,30707 A49 62,5 69, ,3 64, ,34167 A53 45,8 60, ,8 60,9 58,3-0,38732 A61 62,5 33, ,6 35,9 50-0,43732 A55 45,8 53, ,2 54,9 58,3-0,4471 A56 45,8 57, ,3 59,3 66,7-0,53188 A65 45,8 51, ,5 38,7 66,7-0,57391 A57 54,2 51, ,4 53,7 58,3-0,58949 A , ,5 54,2 41,7-0,59583 A58 58,3 51, ,8 55,3 75-0,64239 A62 45,8 42, ,9 69,9 66,7-0,65471 A , ,1 49,5 66,7-0,66051 A63 33,3 55, ,2 59,7 41,7-0,66395 A64 37,5 53, ,1 49,3 58,3-0,71377 A67 45,8 53, ,1 54,2 50-0,77464 A66 41,7 37, ,6 59,7 50-0,78641 A68 29,2 26, ,7 43,3 41,7-0,8192 A70 20,8 35, , ,7-0,89946 A69 33,3 48, ,3 52,3 33,3-0,91105 Crit6 Crit1 Crit3 Crit2 Crit5 Crit4 NetFlows A4 63, , , , A , , , A5 55, , , A7 61, , ,4 91,7 0, A2 71, , ,4 91,7 0, A6 58, ,2 95,8 96, ,72029 A ,9 87,5 96, , A9 62, , ,3 91,7 0, A10 53, , , , A , , ,67337 A13 61, ,4 87,5 92, , A14 55, ,4 91,7 96, ,60163 A12 72, ,2 87,5 89, ,59058 A11 67, ,7 87,5 92, , A15 52, ,7 91,7 92, , A16 65, ,7 91,7 89, , A ,4 91,7 85,7 83,3 0, A17 50, ,4 91,7 89, , A20 58, ,6 83,3 89, , A19 46, ,7 91,7 96, , A21 42, ,7 91,7 92, , A22 46, ,6 87, ,3 0, A23 39, ,7 91,7 92, , A ,7 83, , A27 54, ,5 79,2 83,9 91,7 0,21721 A25 41, ,1 87,5 80,4 91,7 0, A30 51, ,2 66,7 85,7 83,3 0, A26 42, ,9 87,5 85, , A28 48, ,5 87,5 80,4 83,3 0, A29 47, ,1 83, , A34 48, ,7 62,5 82,1 66,7 0, A36 52, ,3 70,8 66,1 66,7-0,00598 A35 47, ,7 66, ,7-0,00906 A ,3 70,8 82,1 75-0,01866 A31 35, ,1 70,8 85,7 83,3-0,02083 A41 65, ,4 66,7 46,4 75-0,04094 A33 46, , ,04783 A38 27, ,3 66,7 82,1 66,7-0,12373 A37 36, ,8 62,5 76,8 91,7-0,13696 A ,5 66,7 71,4 83,3-0,14855 A40 44, ,5 58,3 69,6 83,3-0,17174 A39 42, ,1 62,5 76,8 66,7-0,17283 A46 58, ,6 58,3 58,9 75-0,19529 A43 34, ,3 66,7 66,1 66,7-0,22572 A50 50, ,2 62,5 64,3 66,7-0,22681 A54 52, ,6 41,7 60,7 75-0,28043 A , ,1 75-0,28696 A , ,7-0,29275 A52 52, ,3 54,2 51,8 66,7-0,29891 A48 46, ,2 58,3 64,3 66,7-0,3 A51 47, , ,9 58,3-0,30036 A44 33, , ,3-0,30707 A49 36, ,4 62,5 69, ,34167 A53 43, ,9 45,8 60,7 58,3-0,38732 A61 53, ,9 62,5 33,9 50-0,43732 A55 48, ,9 45,8 53,6 58,3-0,4471 A56 42, ,3 45,8 57,1 66,7-0,53188 A65 48, ,7 45,8 51,8 66,7-0,57391 A57 38, ,7 54,2 51,8 58,3-0,58949 A59 36, , ,4 41,7-0,59583 A58 26, ,3 58,3 51,8 75-0,64239 A62 33, ,9 45,8 42,9 66,7-0,65471 A60 35, , ,2 66,7-0,66051 A63 23, ,7 33,3 55,4 41,7-0,66395 A64 24, ,3 37,5 53,6 58,3-0,71377 A67 30, ,2 45,8 53,6 50-0,77464 A66 22, ,7 41,7 37,5 50-0,78641 A68 35, ,3 29,2 26,8 41,7-0,8192 A70 17, ,8 35,7 66,7-0,89946 A69 22, ,3 33,3 48,2 33,3-0,91105 (a) Netflow-Angle (b) Netflow-Weight Best cities ranking 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 18
19 Best cities ranking representations Crit2 Crit5 Crit1 Crit6 Crit3 Crit4 NetFlows A6 95,8 96, ,9 91, ,72029 A15 91,7 92, ,7 91, , A ,7 94, , A , ,3 94, , A , , ,67337 A19 91,7 96, ,7 91, , A26 87,5 85, ,3 85, , A21 91,7 92, ,9 91, , A24 91,7 83, , A25 87,5 80, ,7 95,1 91,7 0, A23 91,7 92, ,3 91, , A22 87, ,7 76,6 83,3 0, A31 70,8 85, ,1 89,1 83,3-0,02083 A32 70,8 82, ,3 75-0,01866 A38 66,7 82, ,7 65,3 66,7-0,12373 A37 62,5 76, ,6 67,8 91,7-0,13696 A34 62,5 82, ,5 63,7 66,7 0, A47 62, ,7-0,29275 A43 66,7 66, ,7 74,3 66,7-0,22572 A33 62, , ,04783 A ,3 73,4 83,3-0,30707 A39 62,5 76, ,9 61,1 66,7-0,17283 A , ,1 75-0,28696 A63 33,3 55, ,2 59,7 41,7-0,66395 A64 37,5 53, ,1 49,3 58,3-0,71377 A58 58,3 51, ,8 55,3 75-0,64239 A66 41,7 37, ,6 59,7 50-0,78641 A49 62,5 69, ,3 64, ,34167 A , ,1 49,5 66,7-0,66051 A70 20,8 35, , ,7-0,89946 A69 33,3 48, ,3 52,3 33,3-0,91105 A , ,5 54,2 41,7-0,59583 A67 45,8 53, ,1 54,2 50-0,77464 A57 54,2 51, ,4 53,7 58,3-0,58949 A53 45,8 60, ,8 60,9 58,3-0,38732 A68 29,2 26, ,7 43,3 41,7-0,8192 A62 45,8 42, ,9 69,9 66,7-0,65471 A56 45,8 57, ,3 59,3 66,7-0,53188 A48 58,3 64, ,1 63,2 66,7-0,3 A55 45,8 53, ,2 54,9 58,3-0,4471 A , ,5 68,8 58,3-0,30036 A65 45,8 51, ,5 38,7 66,7-0,57391 A42 66,7 71, ,5 83,3-0,14855 A52 54,2 51, ,1 56,3 66,7-0,29891 A61 62,5 33, ,6 35,9 50-0,43732 A40 58,3 69, ,9 90,5 83,3-0,17174 A50 62,5 64, ,6 75,2 66,7-0,22681 A54 41,7 60, ,1 76,6 75-0,28043 A46 58,3 58, ,6 55,6 75-0,19529 A36 70,8 66, ,4 80,3 66,7-0,00598 A41 66,7 46, ,8 82,4 75-0,04094 A35 66, ,3 81,7 91,7-0,00906 A27 79,2 83, ,2 81,5 91,7 0,21721 A12 87,5 89, ,6 97, ,59058 A16 91,7 89, ,2 91, , A28 87,5 80, ,2 81,5 83,3 0, A11 87,5 92, ,3 91, , A20 83,3 89, ,8 85, , A , ,3 97,2 91,7 0, A30 66,7 85, ,5 72,2 83,3 0, A , ,5 97,2 91,7 0, A14 91,7 96, ,1 94, ,60163 A13 87,5 92, ,3 94, , A1 87,5 96, , , A , ,7 97, , A , ,7 97,2 91,7 0, A , , , A29 83, ,3 83,1 75 0, A18 91,7 85, ,4 83,3 0, A17 91,7 89, ,3 94, , Crit4 Crit3 Crit2 Crit5 Crit6 Crit1 NetFlows A ,4 91,7 89,3 50,3 80 0, A18 83,3 94,4 91,7 85, , A ,1 83, ,3 75 0, A , , , A7 91,7 97, ,4 61,7 85 0, A , ,4 63,7 85 0, A ,9 87,5 96, , A ,4 87,5 92,9 61,3 85 0, A ,4 91,7 96,4 55,1 80 0,60163 A9 91,7 97, ,3 62,5 85 0, A30 83,3 72,2 66,7 85,7 51,5 80 0, A2 91,7 97, ,4 71,3 80 0, A ,6 83,3 89,3 58,8 80 0, A ,7 87,5 92,9 67,3 80 0, A28 83,3 81,5 87,5 80,4 48,2 65 0, A ,7 91,7 89,3 65,2 70 0, A ,2 95,8 96,4 58,9 95 0,72029 A ,7 91,7 92,9 52,7 85 0, A , ,7 90 0, A , ,9 53,3 90 0, A ,2 87,5 89,3 72,6 70 0,59058 A , , ,67337 A ,7 91,7 96,4 46,7 80 0, A27 91,7 81,5 79,2 83,9 54,2 65 0,21721 A ,9 87,5 85,7 42,3 70 0, A ,7 91,7 92,9 42,9 85 0, A ,7 83, , A25 91,7 95,1 87,5 80,4 41,7 80 0, A ,7 91,7 92,9 39,3 85 0, A22 83,3 76,6 87, ,7 95 0, A35 91,7 81,7 66, ,3 60-0,00906 A31 83,3 89,1 70,8 85,7 35,1 75-0,02083 A ,4 66,7 46,4 65,8 45-0,04094 A ,3 70,8 82, ,01866 A36 66,7 80,3 70,8 66,1 52,4 60-0,00598 A38 66,7 65,3 66,7 82,1 27,7 90-0,12373 A ,6 58,3 58,9 58,6 55-0,19529 A37 91,7 67,8 62,5 76,8 36,6 80-0,13696 A ,6 41,7 60,7 52,1 30-0,28043 A50 66,7 75,2 62,5 64,3 50,6 35-0,22681 A40 83,3 90,5 58,3 69,6 44,9 50-0,17174 A34 66,7 63,7 62,5 82,1 48,5 85 0, A47 66, , ,29275 A ,9 62,5 33,9 53,6 50-0,43732 A43 66,7 74,3 66,7 66,1 34,7 80-0,22572 A52 66,7 56,3 54,2 51,8 52,1 60-0,29891 A42 83,3 77,5 66,7 71, ,14855 A65 66,7 38,7 45,8 51,8 48,5 20-0,57391 A , ,1 80-0,04783 A51 58,3 68, ,9 47,5 55-0,30036 A55 58,3 54,9 45,8 53,6 48,2 55-0,4471 A44 83,3 73, ,3 70-0,30707 A39 66,7 61,1 62,5 76,8 42,9 80-0,17283 A48 66,7 63,2 58,3 64,3 46,1 60-0,3 A56 66,7 59,3 45,8 57,1 42,3 50-0,53188 A , , ,28696 A62 66,7 69,9 45,8 42,9 33,9 40-0,65471 A68 41,7 43,3 29,2 26,8 35,7 50-0,8192 A53 58,3 60,9 45,8 60,7 43,8 65-0,38732 A57 58,3 53,7 54,2 51,8 38,4 55-0,58949 A ,2 45,8 53,6 30,1 25-0,77464 A59 41,7 54, ,4 36,5 55-0,59583 A69 33,3 52,3 33,3 48,2 22,3 25-0,91105 A70 66, ,8 35,7 17,3 30-0,89946 A60 66,7 49, ,2 35,1 55-0,66051 A ,4 62,5 69,6 36,3 50-0,34167 A ,7 41,7 37,5 22,6 50-0,78641 A63 41,7 59,7 33,3 55,4 23,2 60-0,66395 A64 58,3 49,3 37,5 53,6 24,1 60-0,71377 A ,3 58,3 51,8 26,8 50-0,64239 (c) Angle-Angle (d) Proximity-Proximity Best cities ranking (cont.) 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 19
20 Case study 2: Environmental Performance Index (EPI) 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 20
21 Case study 2: Environmental Performance Index (EPI) Analyse visuelle globale Delta: 57.31% Argentina India Indonesia Brazil Saudi Arabia South Africa Agriculture Air United Quality States of America Canada Water Sanitation Turkey Biodiversity Health Habitat Impacts Mexico FisheriesClimate Water Forests Energy Resources Russia France United Australia Kingdom China South Korea Japan Germany Italy GAIA plane for the EPI 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 21
22 Environmental 2nd International MCDA Performance Workshop on PROMETHEE:Research Index and Case Studies 22 EPI representations Crit3 Crit1 Crit4 Crit7 Crit8 Crit6 Crit5 Crit9 Crit2 NetFlows 0, , , , , , , , , A1 0 A3 0, , , , , , , , , A2 0, , , , , , , , , A5 0, , , , , , , , , ,37963 A4-0, , , , , , , , , , A7 0, , , , , , , , , , A6 0, , , , , , , , , ,225 A8 0, , , , , , , , , A9 0, , , , , , , , ,02963 A15-0, , , , , , , , , ,06759 A11-0, , , , , , , , ,14352 A14-0, , , , , , , , ,17315 A10 0, , , , , , , , ,18056 A , , , , , ,18518 A13-0, , , , , , ,23611 A18-0, , , , , , , ,34537 A12-0, , , , , , , ,3537 A , , , , , , ,51667 A19-0, , , , , , , , , ,75278 (a) Netflow-Angle Crit1 Crit2 Crit3 Crit5 Crit6 Crit9 Crit7 Crit8 Crit4 NetFlows 0, , , , , , , , , A1 0 A3 0, , , , , , , , , A2-0, , , , , , , , , A5 0, , , , , , , , , ,37963 A4-0, , , , , , , , , , A7 0, , , , , , , , , , A6-0, , , , , , , , , ,225 A8 0, , , , , , , , , A9-0, , , , , , , , ,02963 A15 0, , , , , , , , , ,06759 A11 0-0, , , , , , , , ,14352 A14 0, , , , , , , , ,17315 A10-0, , , , , , , , ,18056 A16 1-0, , , , , ,18518 A13 0, , , , , , ,23611 A , , , , , , , ,34537 A12-0, , , , , , , ,3537 A17-0, , , , , , ,51667 A19-0, , , , , , , , , ,75278 (b) Netflow-Weight
23 Environmental 2nd International Performance MCDA WorkshopIndex on PROMETHEE:Research (cont.) and Case Studies 23 EPI representations Crit3 Crit1 Crit4 Crit7 Crit8 Crit6 Crit5 Crit9 Crit2 NetFlows 0, , , , , , , , , A3 1 A1 0, , , , , , , , , A7 0, , , , , , , , , , A5 0, , , , , , , , , ,37963 A8 0, , , , , , , , , A9 0, , , , , , , , ,02963 A , , , , , ,18518 A13-0, , , , , , ,23611 A15-0, , , , , , , , , ,06759 A19-0, , , , , , , , , ,75278 A , , , , , , ,51667 A12-0, , , , , , , ,3537 A11-0, , , , , , , , ,14352 A14-0, , , , , , , , ,17315 A18-0, , , , , , , ,34537 A10 0, , , , , , , , ,18056 A6 0, , , , , , , , , ,225 A4-0, , , , , , , , , , A2 0, , , , , , , , , (c) Angle-Angle Crit3 Crit2 Crit9 Crit5 Crit6 Crit8 Crit1 Crit4 Crit7 NetFlows 0, , , , , , , , , A3 1 A1 0, , , , , , , , , A2 0, , , , , , , , , A7 0, , , , , , , , , , A5 0, , , , , , , , , ,37963 A8 0, , , , , , , , , A4-0, , , , , , , , , , A6 0, , , , , , , , , ,225 A9 0, , , , , , , , ,02963 A10 0, , , , , , , , ,18056 A16 0-0, , , , , ,18518 A13-0, , , , , , ,23611 A18-0, , , , , , , ,34537 A15-0, , , , , , , , , ,06759 A14-0, , , , , , , , ,17315 A11-0, , , , , , , , ,14352 A12-0, , , , , , , ,3537 A , , , , , , ,51667 A19-0, , , , , , , , , ,75278 (d) Proximity-Proximity
24 Comparing the representation with the ratio R Multicriteria-enriched tables can still hold ordinal properties Best cities ranking subset Best cities ranking Environmental Performance Index Evaluations Unicriterion Flows Evaluations Unicriterion Flows Evaluations Unicriterion flows Nabla R Nabla R Nabla R Nabla R Nabla R Nabla R GA Best ,00% ,00% ,00% ,00% ,00% ,00% GA Worst 149 0,00% 205 0,00% ,00% ,00% 643 0,00% 838 0,00% Netflow-Angle ,39% ,48% ,35% ,21% ,74% ,42% Netflow-Weight ,95% ,49% ,55% ,98% ,55% ,85% Angle-Angle ,11% ,98% ,45% ,83% ,61% ,97% Proxi-Proxi ,59% ,95% ,06% ,93% ,11% ,34% 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 24
25 Conclusion Multicriteria-enriched evaluation table can give an interesting insights into a problem Development of the -indicator and the ratio R to evaluate and compare the representations The PROMETHEE-based tables still hold good ordinal properties while giving multicriteria information 2nd International MCDA Workshop on PROMETHEE:Research and Case Studies 25
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