Outranking Methods: Promethee I and Promethee II

Models	Processor	Hard Disk Capacity	Operating System	RAM	Screen Size	Brand	Color
Model 1	I3	512GB	DOS	4GB	14 Inch	HP	Black
Model 2	I5	1TB	Linux	4GB	15.6 Inch	Acer	Black
Model 3	I5	2TB	Windows	8GB	15.6 Inch	Lenovo	Gold
Model 4	I7	2TB	Windows	16GB	17.3 Inch	Asus	Silver
Model 5	I5	1TB	Windows	8GB	15.6 Inch	HP	Silver
Model 6	I3	512GB	Linux	4GB	15.6 Inch	Dell	Black

[i] (Source: Online shopping Websites and electronic stores)

AHP methodology (*Source:*Kolios, et al., 2016)

Table 3

Pair-wise comparison matrix

Comparisons	Processor	Hard disk capacity	Operating system	RAM	Screen size	Brand	Color
Processor	1	5	7	3	2	7	9
Hard disk capacity	1/5	1	3	1/3	1/3	2	5
Operating system	1/7	1/3	1	1/5	1/3	1/3	3
RAM	1/3	3	5	1	2	3	9
Screen size	1/2	3	3	1/2	1	3	7
Brand	1/7	1/2	3	1/3	1/3	1	5
Color	1/9	1/5	1/3	1/9	1/7	1/5	1
Total	2.43016	13.03333	22.33333	5.47778	6.14286	16.53333	39

[i] (Source: Own elaboration)

Table 4

Normalized pair-wise comparison matrix

Comparisons	Processor	Hard disk capacity	Operating system	RAM	Screen size	Brand	Color	Priority Vector	Weight %
Processor	0.41150	0.38363	0.31343	0.54767	0.32558	0.42339	0.23077	0.37657	37.657
Hard disk capacity	0.08230	0.07673	0.13433	0.06085	0.05426	0.12097	0.12821	0.09395	9.395
Operating system	0.05879	0.02558	0.04478	0.03651	0.05426	0.02016	0.07692	0.04529	4.529
RAM	0.13717	0.23018	0.22388	0.18256	0.32558	0.18145	0.23077	0.21594	21.594
Screen size	0.20575	0.23018	0.13433	0.09128	0.16279	0.18145	0.17949	0.16932	16.932
Brand	0.05879	0.03836	0.13433	0.06085	0.05426	0.06048	0.12821	0.07647	7.647
Color	0.04572	0.01535	0.01493	0.02028	0.02326	0.01210	0.02564	0.02247	2.247
Total	1	1	1	1	1	1	1	1	100

[i] (Source: Own elaboration)

Table 5

Saaty's pair-wise comparison scale

Saaty's pair wise comparison scale	Compare factor of i & j
1	Equal Importance
3	Moderate Importance
5	Strong Importance
7	Very Strong or Demonstrated Importance
9	Extreme Importance
2, 4, 6, 8	Intermediate values when compromise is needed

[i] (Source: Saaty, 1980)

Table 6

Randomly generated consistency index (RI) values

n	1	2	3	4	5	6	7	8	9	10	11	12
RI	0.00	0.00	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49	1.51	1.58

[i] (Source:Saaty, 1980)

PROMETHEE methodology (*Source:*Kolios, et al., 2016)

Table 7

Evaluation matrix

Models	Processor	Hard disk capacity	Operating system	RAM	Screen size	Brand	Color
Model 1	3	5	3	5	3	9	3
Model 2	5	7	5	5	7	3	3
Model 3	5	9	9	7	7	7	5
Model 4	7	9	9	9	9	2	9
Model 5	5	7	9	7	7	9	9
Model 6	3	5	5	5	7	5	3
Max	7	9	9	9	9	9	9
Min	3	5	3	5	3	2	3

[i] (Source: Own elaboration)

Table 8

Hwang ang Yoon comparison scale

Qualitative Estimation	Bad	Good	Average	Very Good	Excellent	Types of Criteria
Quantitative Estimation	1	3	5	7	9	Max
Quantitative Estimation	9	7	5	3	1	Min

[i] (Source:Hwang and Yoon, 1981)

Table 9

Normalized decision matrix

Models	Processor	Hard disk capacity	Operating system	RAM	Screen size	Brand	Color
Model 1	0	0	0	0	0	1	0
Model 2	0.5	0.5	0.33333	0	0.66667	0.14286	0
Model 3	0.5	1	1	0.5	0.66667	0.71429	0.33333
Model 4	1	1	1	1	1	0	1
Model 5	0.5	0.5	1	0.5	0.66667	1	1
Model 6	0	0	0.33333	0	0.66667	0.42857	0

[i] (Source: Own elaboration)

Table 10

Evaluative difference of i^th alternatives with respect other alternatives

Evaluative difference	Processor	Hard disk capacity	Operating system	RAM	Screen size	Brand	Color
Model 1
D (M1-M2)	−0.5	−0.5	−0.33333	0	−0.66667	0.85714	0
D (M1-M3)	−0.5	−1	−1	−0.5	−0.66667	0.28571	−0.33333
D (M1-M4)	−1	−1	−1	−1	−1	1	−1
D (M1-M5)	−0.5	−0.5	−1	−0.5	−0.66667	0	−1
D (M1-M6)	0	0	−0.33333	0	−0.66667	0.57143	0
Model 2
D (M2-M1)	0.5	0.5	0.33333	0	0.66667	−0.85714	0
D (M2-M3)	0	−0.5	−0.66667	−0.5	0	−0.57143	−0.33333
D (M2-M4)	−0.5	−0.5	−0.66667	−1	−0.33333	0.14286	−1
D (M2-M5)	0	0	−0.66667	−0.5	0	−0.85714	−1
D (M2-M6)	0.5	0.5	0	0	0	−0.28571	0
Model 3
D (M3-M1)	0.5	1	1	0.5	0.66667	−0.28571	0.33333
D (M3-M2)	0	0.5	0.66667	0.5	0	0.57143	0.33333
D (M3-M4)	−0.5	0	0	−0.5	−0.33333	0.71429	−0.66667
D (M3-M5)	0	0.5	0	0	0	−0.28571	−0.66667
D (M3-M6)	0.5	1	0.66667	0.5	0	0.28571	0.33333
Model 4
D (M4-M1)	1	1	1	1	1	−1	1
D (M4-M2)	0.5	0.5	0.66667	1	0.33333	−0.14286	1
D (M4-M3)	0.5	0	0	0.5	0.33333	−0.71429	0.66667
D (M4-M5)	0.5	0.5	0	0.5	0.33333	−1	0
D (M4-M6)	1	1	0.66667	1	0.33333	−0.42857	1
Model 5
D (M5-M1)	0.5	0.5	1	0.5	0.66667	0	1
D (M5-M2)	0	0	0.66667	0.5	0	0.85714	1
D (M5-M3)	0	−0.5	0	0	0	0.28571	0.66667
D (M5-M4)	−0.5	−0.5	0	−0.5	−0.33333	1	0
D (M5-M6)	0.5	0.5	0.66667	0.5	0	0.57143	1
Model 6
D (M6-M1)	0	0	0.33333	0	0.66667	−0.57143	0
D (M6-M2)	−0.5	−0.5	0	0	0	0.28571	0
D (M6-M3)	−0.5	−1	−0.66667	−0.5	0	−0.28571	−0.33333
D (M6-M4)	−1	−1	−0.66667	−1	−0.33333	0.42857	−1
D (M6-M5)	−0.5	−0.5	−0.66667	−0.5	0	−0.57143	−1

[i] (Source: Own elaboration)

Table 11

Preference function, Pj (Ma, Mb)

Weights (w_j)	0.37657	0.09395	0.04529	0.21594	0.16932	0.07647	0.02247
Evaluative difference	Processor	Hard disk capacity	Operating system	RAM	Screen size	Brand	Color
Model 1
P (M1, M2)	0	0	0	0	0	0.85714	0
P (M1, M3)	0	0	0	0	0	0.28571	0
P (M1, M4)	0	0	0	0	0	1	0
P (M1, M5)	0	0	0	0	0	0	0
P (M1, M6)	0	0	0	0	0	0.57143	0
Model 2
P (M2, M1)	0.5	0.5	0.33333	0	0.66667	0	0
P (M2, M3)	0	0	0	0	0	0	0
P (M2, M4)	0	0	0	0	0	0.14286	0
P (M2, M5)	0	0	0	0	0	0	0
P (M2, M6)	0.5	0.5	0	0	0	0	0
Model 3
P (M3, M1)	0.5	1	1	0.5	0.66667	0	0.33333
P (M3, M2)	0	0.5	0.66667	0.5	0	0.57143	0.33333
P (M3, M4)	0	0	0	0	0	0.71429	0
P (M3, M5)	0	0.5	0	0	0	0	0
P (M3, M6)	0.5	1	0.66667	0.5	0	0.28571	0.33333
Model 4
P (M4, M1)	1	1	1	1	1	0	1
P (M4, M2)	0.5	0.5	0.66667	1	0.33333	0	1
P (M4, M3)	0.5	0	0	0.5	0.33333	0	0.66667
P (M4, M5)	0.5	0.5	0	0.5	0.33333	0	0
P (M4, M6)	1	1	0.66667	1	0.33333	0	1
Model 5
P (M5, M1)	0.5	0.5	1	0.5	0.66667	0	1
P (M5, M2)	0	0	0.66667	0.5	0	0.85714	1
P (M5, M3)	0	0	0	0	0	0.28571	0.66667
P (M5, M4)	0	0	0	0	0	1	0
P (M5, M6)	0.5	0.5	0.66667	0.5	0	0.57143	1
Model 6
P (M6, M1)	0	0	0.33333	0	0.66667	0	0
P (M6, M2)	0	0	0	0	0	0.28571	0
P (M6, M3)	0	0	0	0	0	0	0
P (M6, M4)	0	0	0	0	0	0.42857	0
P (M6, M5)	0	0	0	0	0	0	0

[i] (Source: Own elaboration)

Table 12

Calculating the aggregated preference, π (Ma, Mb)

Weights	0.37657	0.09395	0.04529	0.21594	0.16932	0.07647	0.02247	1
								Aggregated preference, π (Ma, Mb)
Model 1
π (M1, M2)	0	0	0	0	0	0.06554	0	0.06554
π (M1, M3)	0	0	0	0	0	0.02185	0	0.02185
π (M1, M4)	0	0	0	0	0	0.07647	0	0.07647
π (M1, M5)	0	0	0	0	0	0	0	0
π (M1, M6)	0	0	0	0	0	0.04370	0	0.04370
Model 2
π (M2, M1)	0.18828	0.04697	0.01510	0	0.11288	0	0	0.36323
π (M2, M3)	0	0	0	0	0	0	0	0
π (M2, M4)	0	0	0	0	0	0.01092	0	0.01092
π (M2, M5)	0	0	0	0	0	0	0	0
π (M2, M6)	0.18828	0.04697	0	0	0	0	0	0.23526
Model 3
π (M3, M1)	0.18828	0.09395	0.04529	0.10797	0.11288	0	0.00749	0.55586
π (M3, M2)	0	0.04697	0.03019	0.10797	0	0.04370	0.00749	0.23632
π (M3, M4)	0	0	0	0	0	0.05462	0	0.05462
π (M3, M5)	0	0.04697	0	0	0	0	0	0.04697
π (M3, M6)	0.18828	0.09395	0.03019	0.10797	0	0.02185	0.00749	0.44973
Model 4
π (M4, M1)	0.37657	0.09395	0.04529	0.21594	0.16932	0	0.02247	0.92353
π (M4, M2)	0.18828	0.04697	0.03019	0.21594	0.05644	0	0.02247	0.56030
π (M4, M3)	0.18828	0	0	0.10797	0.05644	0	0.01498	0.36767
π (M4, M5)	0.18828	0.04697	0	0.10797	0.05644	0	0	0.39967
π (M4, M6)	0.37657	0.09395	0.03019	0.21594	0.05644	0	0.02247	0.79555
Model 5
π (M5, M1)	0.18828	0.04697	0.04529	0.10797	0.11288	0	0.02247	0.52386
π (M5, M2)	0	0	0.03019	0.10797	0.00000	0.06554	0.02247	0.22617
π (M5, M3)	0	0	0	0	0	0.02185	0.01498	0.03683
π (M5, M4)	0	0	0	0	0	0.07647	0	0.07647
π (M5, M6)	0.18828	0.04697	0.03019	0.10797	0	0.04370	0.02247	0.43958
Model 6
π (M6, M1)	0	0	0.01510	0	0.11288	0	0	0.12798
π (M6, M2)	0	0	0	0	0	0.02185	0	0.02185
π (M6, M3)	0	0	0	0	0	0	0	0
π (M6, M4)	0	0	0	0	0	0.03277	0	0.03277
π (M6, M5)	0	0	0	0	0	0	0	0

[i] (Source: Own elaboration)

Table 13

Aggregate preference function matrix

Models	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
Model 1	-	0.06554	0.02185	0.07647	0	0.04370
Model 2	0.36323	-	0	0.01092	0	0.23526
Model 3	0.55586	0.23632	-	0.05462	0.04697	0.44973
Model 4	0.92353	0.56030	0.36767	-	0.39967	0.79555
Model 5	0.52386	0.22617	0.03683	0.07647	-	0.43958
Model 6	0.12798	0.02185	0	0.03277	0	-

[i] (Source: Own elaboration)

Table 14

Determination of leaving and entering outranking flow (PROMETHEE I)

Models	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Leaving flow ϕ+
Model 1	-	0.06554	0.02185	0.07647	0	0.04370	0.20756
Model 2	0.36323	-	0	0.01092	0	0.23526	0.60942
Model 3	0.55586	0.23632	-	0.05462	0.04697	0.44973	1.34350
Model 4	0.92353	0.56030	0.36767	-	0.39967	0.79555	3.04672
Model 5	0.52386	0.22617	0.03683	0.07647	-	0.43958	1.30291
Model 6	0.12798	0.02185	0	0.03277	0	-	0.18260
Entering flow ϕ−	2.49446	1.11018	0.42635	0.25125	0.44664	1.96382

[i] (Source: Own elaboration)

Table 15

Determination of leaving and entering outranking flow (PROMETHEE II)

Models	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6	Leaving flow ϕ+
Model 1	-	0.06554	0.02185	0.07647	0.00000	0.04370	0.04151
Model 2	0.36323	-	0.00000	0.01092	0.00000	0.23526	0.12188
Model 3	0.55586	0.23632	-	0.05462	0.04697	0.44973	0.26870
Model 4	0.92353	0.56030	0.36767	-	0.39967	0.79555	0.60934
Model 5	0.52386	0.22617	0.03683	0.07647	-	0.43958	0.26058
Model 6	0.12798	0.02185	0.00000	0.03277	0.00000	-	0.03652
Entering flow ϕ−	0.49889	0.22204	0.08527	0.05025	0.08933	0.39276

[i] (Source: Own elaboration)

Table 16

Net outranking flow of the alternatives

Models	Leaving flow ϕ+	Entering flow ϕ−	Net flow ϕ
Model 1	0.04151	0.49889	−0.45738
Model 2	0.12188	0.22204	−0.10015
Model 3	0.26870	0.08527	0.18343
Model 4	0.60934	0.05025	0.55909
Model 5	0.26058	0.08933	0.17125
Model 6	0.03652	0.39276	−0.35624

[i] (Source: Own elaboration)

Table 17

Comparisons of the laptop models among each other

Sl. No.	Comparisons	Sl. No.	Comparisons
1	Model 2 P Model 1	9	Model 2 P Model 6
2	Model 3 P Model 1	10	Model 4 P Model 3
3	Model 4 P Model 1	11	Model 3 P Model 5
4	Model 5 P Model 1	12	Model 3 P Model 6
5	Model 1 R Model 6	13	Model 4 P Model 5
6	Model 3 P Model 2	14	Model 4 P Model 6
7	Model 4 P Model 2	15	Model 5 P Model 6
8	Model 5 P Model 2

[i] (Source: Own elaboration)

Table 18

Ranking of the laptop models

Models	Net flow ϕ	Ranking
Model 1	−0.45738	Rank 6
Model 2	−0.10015	Rank 4
Model 3	0.18343	Rank 2
Model 4	0.55909	Rank 1
Model 5	0.17125	Rank 3
Model 6	−0.35624	Rank 5

[i] (Source: Own elaboration)

References

Authors

Metrics

Articles in this issue

DOI: https://doi.org/10.2478/fman-2020-0008 | Journal eISSN: 2300-5661 | Journal ISSN: 2080-7279

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Language: English

Page range: 93 - 110

Published on: Jul 9, 2020

Published by: Warsaw University of Technology

In partnership with: Paradigm Publishing Services

Keywords:

PROMETHEE I,

PROMETHEE II,

AHP,

MCDM,

laptop models

JEL:

C61,

C83,

D81,

M11

Related subjects:

Computer sciences,

Business computing,

Business and economics,

Business management,

Management accounting, financial controlling, cost calculation, investment

© 2020 Shankha Shubhra Goswami, published by Warsaw University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 12 (2020): Issue 1 (January 2020)

Outranking Methods: Promethee I and Promethee II

Figures & Tables

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Figure 1

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Table 4

Table 5

Table 6

Figure 2

Table 7

Table 8

Table 9

Table 10

Table 11

Table 12

Table 13

Table 14

Table 15

Table 16

Table 17

Table 18

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