Multi-Attribute Decision Making with VIKOR Method for Any Purpose Decision
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The document discusses the implementation of a decision support system using the VIKOR method for multi-attribute decision making. It highlights the method's efficiency in determining the best alternatives from predefined criteria, demonstrating the process with specific examples and calculations. The study concludes that the VIKOR method is effective for aiding decision-making through a straightforward and computationally efficient evaluation process.
![1
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd
1234567890 ‘’“”
1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034
Multi-Attribute Decision Making with VIKOR Method for
Any Purpose Decision
Dodi Siregar1
, Heri Nurdiyanto2
, S Sriadhi3
, Diana Suita4
, Ummul Khair1
,
Robbi Rahim5*
, Darmawan Napitupulu6
, Achmad Fauzi7
, Abdurrozzaq
Hasibuan8
, M Mesran9
and Andysah Putera Utama Siahaan4
1
Department of Informatics, Universitas Harapan Medan, Indonesia
2
Department of Informatics, STMIK Dharma Wacana, Indonesia
3
Department of Electrical Engineering, Universitas Negeri Medan, Indonesia
4
Department of Civil Engineering, Universitas Harapan Medan, Indonesia
5
School of Computer and Communication Engineering, Universiti Malaysia Perlis,
Malaysia
6
Research Center for Quality System and Testing Technology, Indonesian Institute
of Sciences, Indonesia
7
Department of Computer Engineering, STMIK Kaputama, Indonesia
8
Department of Industrial Engineering, Universitas Islam Sumatera Utara, Indonesia
9
Department of Informatics, STMIK Budi Darma, Indonesia
*usurobbi85@zoho.com
Abstract. Implementation of Decision Support System for various purposes now can facilitate
policy makers to get the best alternative from a variety of predefined criteria, one of the
methods used in the implementation of Decision Support System is VIKOR (Vise
Kriterijumska Optimizacija I Kompromisno Resenje), VIKOR method in this research got the
best results with an efficient and easily understood process computationally, it is expected that
the results of this study facilitate various parties to develop a model any solutions.
1. Introduction
Decision support systems utilize private resources in a manner with computer skills to improve
decision results, so this is a computer-based support system for decision-making that deals with semi-
issues structured [1] [2]. Decision-making is always correlated with the uncertainty of the results of
decisions taken, to reduce this uncertainty factor, the decision requires valid information about the
conditions that have been, and may occur, then processed the information into several alternative
problems solving as a material consideration in deciding the steps to be implemented, so that the
decision taken is expected to provide maximum benefits [3].
The decision support system that will present in this research uses VIKOR method which aims to
gather information about all data related to multiple attributes and multiple-criteria [4]. The use of
VIKOR method is used because the method it can choose highly effective and efficient criteria for
determining decision outcomes with multiple attributes and multiple-criteria [4] [5] [6]. VIKOR is a
multiple attribute decision-making method used to solve problems in discrete space [7]. Therefore, in
MADM is usually used to perform assessment or selection of several alternatives in a limited number,](https://image.slidesharecdn.com/siregar2018j-180627132223/85/Multi-Attribute-Decision-Making-with-VIKOR-Method-for-Any-Purpose-Decision-2-320.jpg)
![2
1234567890 ‘’“”
1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034
the process of multiple attribute decision making in this paper shows the calculation of VIKOR
method gradually with 25 alternatives and five criteria to determine the accuracy of the process of
VIKOR.
2. Methodology
Some previous studies which discussed the VIKOR method is Papathanasiou [7], Papathanasiou
makes web-based application of TOPSIS and VIKOR MCDM, the policy makers can choose 2 (two)
different decision result from application, and also another researcher Nisel [8] analyzed the
application of VIKOR method to determine the rank of graduation from business program students,
and many other studies discussing experimental results with VIKOR and its combination, from several
types of research it was observed that VIKOR could arrange for many alternatives, so it can be
assumed that the VIKOR algorithm is still relevant to use and in this research VIKOR method is
calculated gradually to facilitate the calculation process for many criteria, many attributes and many
alternatives.
The VIKOR method focuses on ranking and chooses from a set of samples with different criteria,
which can help decision makers to get a final determination [4].
VIKOR is a method for optimizing/optimizing multiple criteria in a complex system. VIKOR's basic
concept is to rank the current samples by looking at the results of the corresponding values or regrets
(R) of each sample. The VIKOR method has applied by some researchers in the case of MCDM [7].
The formula of the VIKOR method is as follows:
1) Normalization of the matrix
=
Information:
Xij = Value of sample i data criteria j
(I = A, B, C, D, E)
(J = 5 criteria)
X*j = Best value in one criterion
X'j = the worst value in one criterion
2) Calculating the S and R-Value
Si=
Wj = weighting criteria
The value of S is achieved from the sum of the result of the multiplication of the criteria weights
by the data in each sample
Ri= Max j [wj x Rij], largest value from [Wj x Rij]
The value of R is the largest value of the multiplication of the weight of the criteria with the
normalized data of each sample
3) Calculates the VIKOR index
Formula= [ ] x V + [ ] x (1-V)
S'= smallest S value (the best value)
S*= the largest S value
R'= the smallest R value
R*= the largest R value
3. Result and Discussion
The analysis of the VIKOR method can be seen gradually in the following test process gradually, for
the first step is to determine the criteria to be given the weight value for VIKOR calculation process,
Table 1 below are the criteria that are used in this paper:](https://image.slidesharecdn.com/siregar2018j-180627132223/85/Multi-Attribute-Decision-Making-with-VIKOR-Method-for-Any-Purpose-Decision-3-320.jpg)
![6
1234567890 ‘’“”
1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034
Figure 1. VIKOR Result
Based on the above graph shows the results of calculations VIKOR method meet proper distribution
with a uniform process.
4. Conclusion
The experiment of the VIKOR method can help to complete effective decision-making because the
concept is straightforward and easy to understand and the computation process is efficient and can
measure the relative performance of various decision alternatives
5. References
[1] Risawandi and R. Rahim, "Study of the Simple Multi-Attribute Rating Technique For Decision
Support," International Journal of Scientific Research in Science and Technology (IJSRST) , vol.
2, no. 6, pp. 491-494, 2016.
[2] Syamsudin and R. Rahim, "Study Approach Technique for Order of Preference by Similarity to
Ideal Solution (TOPSIS)," International Journal of Recent Trends in Engineering & Research,
vol. 3, no. 3, pp. 268-285, 2017.
[3] Mesran, G. Ginting, R. Rahim and Suginam, "Implementation of Elimination and Choice
Expressing Reality (ELECTRE) Method in Selecting the Best Lecturer (Case Study STMIK BUDI
DARMA)," International Journal of Engineering Research & Technology (IJERT), vol. 6, no. 2,
pp. 141-144, 2017.
[4] C. T. Sasanka and K. Ravindra, "Implementation of VIKOR Method for Selection of Magnesium
Alloy to Suit Automotive Applications," International Journal of Advanced Science and
Technology, vol. 83, pp. 49-58, 2015.
[5] C.-H. Wang and C.-T. Pang, "Using VIKOR Method for Evaluating Service Quality of Online
Auction under Fuzzy Environment," International Journal of Computer Science Engineering and
Technology, vol. 1, no. 6, pp. 307-314, 2011.
[6] M. Xue, X. Tang and N. Feng, "An Extended VIKOR Method for Multiple Attribute Decision
Analysis with Bidimensional Dual Hesitant Fuzzy Information," Mathematical Problems in
Engineering, vol. 2016, pp. 1-16, 2016.
[7] J. Papathanasiou, N. Ploskas, T. Bournaris and B. Manos, "A Decision Support System for
Multiple Criteria Alternative Ranking Using TOPSIS and VIKOR: A Case Study on Social
Sustainability in Agriculture," in International Conference on Decision Support System
Technology, Belgium, 2016.
[8] S. Nisel, "An Extended VIKOR Method for Ranking Online Graduate Business Programs,"
International Journal of Information and Education Technology, vol. 4, no. 1, pp. 103-107, 2014.](https://image.slidesharecdn.com/siregar2018j-180627132223/85/Multi-Attribute-Decision-Making-with-VIKOR-Method-for-Any-Purpose-Decision-7-320.jpg)
Multi-Attribute Decision Making with VIKOR Method for Any Purpose Decision
- 1. Journal of Physics: Conference Series PAPER • OPEN ACCESS Multi-Attribute Decision Making with VIKOR Method for Any Purpose Decision To cite this article: Dodi Siregar et al 2018 J. Phys.: Conf. Ser. 1019 012034 View the article online for updates and enhancements. This content was downloaded from IP address 36.68.108.25 on 27/06/2018 at 13:17
- 2. 1 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1234567890 ‘’“” 1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034 Multi-Attribute Decision Making with VIKOR Method for Any Purpose Decision Dodi Siregar1 , Heri Nurdiyanto2 , S Sriadhi3 , Diana Suita4 , Ummul Khair1 , Robbi Rahim5* , Darmawan Napitupulu6 , Achmad Fauzi7 , Abdurrozzaq Hasibuan8 , M Mesran9 and Andysah Putera Utama Siahaan4 1 Department of Informatics, Universitas Harapan Medan, Indonesia 2 Department of Informatics, STMIK Dharma Wacana, Indonesia 3 Department of Electrical Engineering, Universitas Negeri Medan, Indonesia 4 Department of Civil Engineering, Universitas Harapan Medan, Indonesia 5 School of Computer and Communication Engineering, Universiti Malaysia Perlis, Malaysia 6 Research Center for Quality System and Testing Technology, Indonesian Institute of Sciences, Indonesia 7 Department of Computer Engineering, STMIK Kaputama, Indonesia 8 Department of Industrial Engineering, Universitas Islam Sumatera Utara, Indonesia 9 Department of Informatics, STMIK Budi Darma, Indonesia *usurobbi85@zoho.com Abstract. Implementation of Decision Support System for various purposes now can facilitate policy makers to get the best alternative from a variety of predefined criteria, one of the methods used in the implementation of Decision Support System is VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje), VIKOR method in this research got the best results with an efficient and easily understood process computationally, it is expected that the results of this study facilitate various parties to develop a model any solutions. 1. Introduction Decision support systems utilize private resources in a manner with computer skills to improve decision results, so this is a computer-based support system for decision-making that deals with semi- issues structured [1] [2]. Decision-making is always correlated with the uncertainty of the results of decisions taken, to reduce this uncertainty factor, the decision requires valid information about the conditions that have been, and may occur, then processed the information into several alternative problems solving as a material consideration in deciding the steps to be implemented, so that the decision taken is expected to provide maximum benefits [3]. The decision support system that will present in this research uses VIKOR method which aims to gather information about all data related to multiple attributes and multiple-criteria [4]. The use of VIKOR method is used because the method it can choose highly effective and efficient criteria for determining decision outcomes with multiple attributes and multiple-criteria [4] [5] [6]. VIKOR is a multiple attribute decision-making method used to solve problems in discrete space [7]. Therefore, in MADM is usually used to perform assessment or selection of several alternatives in a limited number,
- 3. 2 1234567890 ‘’“” 1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034 the process of multiple attribute decision making in this paper shows the calculation of VIKOR method gradually with 25 alternatives and five criteria to determine the accuracy of the process of VIKOR. 2. Methodology Some previous studies which discussed the VIKOR method is Papathanasiou [7], Papathanasiou makes web-based application of TOPSIS and VIKOR MCDM, the policy makers can choose 2 (two) different decision result from application, and also another researcher Nisel [8] analyzed the application of VIKOR method to determine the rank of graduation from business program students, and many other studies discussing experimental results with VIKOR and its combination, from several types of research it was observed that VIKOR could arrange for many alternatives, so it can be assumed that the VIKOR algorithm is still relevant to use and in this research VIKOR method is calculated gradually to facilitate the calculation process for many criteria, many attributes and many alternatives. The VIKOR method focuses on ranking and chooses from a set of samples with different criteria, which can help decision makers to get a final determination [4]. VIKOR is a method for optimizing/optimizing multiple criteria in a complex system. VIKOR's basic concept is to rank the current samples by looking at the results of the corresponding values or regrets (R) of each sample. The VIKOR method has applied by some researchers in the case of MCDM [7]. The formula of the VIKOR method is as follows: 1) Normalization of the matrix = Information: Xij = Value of sample i data criteria j (I = A, B, C, D, E) (J = 5 criteria) X*j = Best value in one criterion X'j = the worst value in one criterion 2) Calculating the S and R-Value Si= Wj = weighting criteria The value of S is achieved from the sum of the result of the multiplication of the criteria weights by the data in each sample Ri= Max j [wj x Rij], largest value from [Wj x Rij] The value of R is the largest value of the multiplication of the weight of the criteria with the normalized data of each sample 3) Calculates the VIKOR index Formula= [ ] x V + [ ] x (1-V) S'= smallest S value (the best value) S*= the largest S value R'= the smallest R value R*= the largest R value 3. Result and Discussion The analysis of the VIKOR method can be seen gradually in the following test process gradually, for the first step is to determine the criteria to be given the weight value for VIKOR calculation process, Table 1 below are the criteria that are used in this paper:
- 4. 3 1234567890 ‘’“” 1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034 Table 1. Criteria and Weight No Criteria Weight (%) 1 C1 30 2 C2 25 3 C3 17 4 C4 20 5 C5 8 The next process is to determine alternatives with values for each criterion: Table 2. Alternative and Criteria Value No Alternative Criteria C1 C2 C3 C4 C5 1 A1 0 21 0 15 0 2 A2 11 23 5 13 3 3 A3 12 10 0 12 0 4 A4 10 15 0 12 0 5 A5 5 9 16 8 0 6 A6 9 8 13 5 0 7 A7 15 14 0 7 0 8 A8 24 12 0 18 0 9 A9 17 17 16 20 0 10 A10 5 8 17 5 6 11 A11 9 7 17 12 8 12 A12 10 10 5 20 0 13 A13 17 22 0 11 0 14 A14 0 12 0 11 0 15 A15 5 8 10 6 7 16 A16 5 8 7 4 0 17 A17 0 0 9 4 0 18 A18 10 14 0 11 0 19 A19 7 5 0 8 0 20 A20 11 15 0 5 0 21 A21 13 9 0 4 0 22 A22 17 20 0 4 0 23 A23 23 20 0 5 0 24 A24 0 0 0 0 0 25 A25 0 0 0 0 0 From table value of each criterion will be normalized data, the result can see as below, with example value Criteria C1 R (A1), C1 = = = 1 R (A2), C1= = = 0.54 R (A1) and R (A2) are samples of normalization calculation of first criterion matrix with alternative 1 and alternative 2, and matrix normalization process is executed for all criteria and alternatives, the final result of matrix normalization process could be seen in Table 3 below:
- 5. 4 1234567890 ‘’“” 1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034 Table 3. Normalization Matrix and Weight No Alternative Criteria C1 C2 C3 C4 C5 1 A1 1 0,08 1 0,25 1 2 A2 0,54 0 0,71 0,35 0,62 3 A3 0,5 0,56 1 0,4 1 4 A4 0,58 0,35 1 0,4 1 5 A5 0,79 0,61 0,06 0,6 1 6 A6 0,62 0,65 0,23 0,75 1 7 A7 0,37 0,39 1 0,65 1 8 A8 0 0,48 1 0,1 1 9 A9 0,29 0,26 0,06 0 1 10 A10 0,79 0,65 0 0,75 0,25 11 A11 0,62 0,69 0 0,4 0 12 A12 0,58 0,56 0,71 0 1 13 A13 0,29 0,04 1 0,45 1 14 A14 1 0,48 1 0,45 1 15 A15 0,79 0,65 0,41 0,7 0,12 16 A16 0,79 0,65 0,58 0,8 1 17 A17 1 1 0,47 0,8 1 18 A18 0,58 0,39 1 0,45 1 19 A19 0,71 0,78 1 0,6 1 20 A20 0,54 0,35 1 0,75 1 21 A21 0,46 0,61 1 0,8 1 22 A22 0,29 0,13 1 0,8 1 23 A23 0,04 0,13 1 0,75 1 24 A24 1 1 1 1 1 25 A25 1 1 1 1 1 After the results obtained from the normalization of criteria and alternatives, the next is to multiply the value of normalization and weight so that the performance as table 4 below: Table 4. Result Normalization x Weight No Alternativ e Criteria C1 C2 C3 C4 C5 1 A1 30 2 17 5 8 2 A2 16,2 0 12,07 7 4,96 3 A3 15 14 17 8 8 4 A4 17,4 8,75 17 8 8 5 A5 23,7 15,25 1,02 12 8 6 A6 18,6 16,25 3,91 15 8 7 A7 11,1 9,75 17 13 8 8 A8 0 12 17 2 8 9 A9 8,7 6,5 1,02 0 8 10 A10 23,7 16,25 0 15 2 11 A11 18,6 17,25 0 8 0 12 A12 17,4 14 12,07 0 8 13 A13 8,7 1 17 9 8 14 A14 30 12 17 9 8 15 A15 23,7 9,75 6,97 14 0,96 16 A16 23,7 16,25 9,86 16 8 17 A17 30 25 7,99 16 8
- 6. 5 1234567890 ‘’“” 1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034 18 A18 17,4 9,75 17 9 8 19 A19 21,3 19,5 17 12 8 20 A20 16,2 8,75 17 15 8 21 A21 13,8 15,25 17 16 8 22 A22 8,7 3,25 17 16 8 23 A23 1,2 3,25 17 15 8 24 A24 30 25 17 20 8 25 A25 30 25 17 20 8 Based on the formula VIKOR method that has been described and from the value of table 3 and table 4 and got the value of Q (VIKOR index) by using formula 3 of VIKOR, the results index value in table 5 below: Table 5. Index VIKOR No Alternative Q Value 1 A1 0,9325 2 A2 0,8135 3 A3 0,4435 4 A4 0,4347 5 A5 0,5879 6 A6 0,4799 7 A7 0,4229 8 A8 0,292 9 A9 0 10 A10 0,78 11 A11 0,3595 12 A12 0,8211 13 A13 0,323 14 A14 0,8416 15 A15 0,5576 16 A16 0,6792 17 A17 0,707 18 A18 0,4478 19 A19 0,6492 20 A20 0,4632 21 A21 0,4968 22 A22 0,384 23 A23 0,3279 24 A24 1 25 A25 1 From the table above obtained the data that the sample (A9) has the smallest index value, and A9 is the best ranking, from the data table 5 above obtained graph of the process of using the VIKOR method for each criterion and alternatives that exist.
- 7. 6 1234567890 ‘’“” 1st International Conference on Green and Sustainable Computing (ICoGeS) 2017 IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1019 (2018) 012034 doi:10.1088/1742-6596/1019/1/012034 Figure 1. VIKOR Result Based on the above graph shows the results of calculations VIKOR method meet proper distribution with a uniform process. 4. Conclusion The experiment of the VIKOR method can help to complete effective decision-making because the concept is straightforward and easy to understand and the computation process is efficient and can measure the relative performance of various decision alternatives 5. References [1] Risawandi and R. Rahim, "Study of the Simple Multi-Attribute Rating Technique For Decision Support," International Journal of Scientific Research in Science and Technology (IJSRST) , vol. 2, no. 6, pp. 491-494, 2016. [2] Syamsudin and R. Rahim, "Study Approach Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)," International Journal of Recent Trends in Engineering & Research, vol. 3, no. 3, pp. 268-285, 2017. [3] Mesran, G. Ginting, R. Rahim and Suginam, "Implementation of Elimination and Choice Expressing Reality (ELECTRE) Method in Selecting the Best Lecturer (Case Study STMIK BUDI DARMA)," International Journal of Engineering Research & Technology (IJERT), vol. 6, no. 2, pp. 141-144, 2017. [4] C. T. Sasanka and K. Ravindra, "Implementation of VIKOR Method for Selection of Magnesium Alloy to Suit Automotive Applications," International Journal of Advanced Science and Technology, vol. 83, pp. 49-58, 2015. [5] C.-H. Wang and C.-T. Pang, "Using VIKOR Method for Evaluating Service Quality of Online Auction under Fuzzy Environment," International Journal of Computer Science Engineering and Technology, vol. 1, no. 6, pp. 307-314, 2011. [6] M. Xue, X. Tang and N. Feng, "An Extended VIKOR Method for Multiple Attribute Decision Analysis with Bidimensional Dual Hesitant Fuzzy Information," Mathematical Problems in Engineering, vol. 2016, pp. 1-16, 2016. [7] J. Papathanasiou, N. Ploskas, T. Bournaris and B. Manos, "A Decision Support System for Multiple Criteria Alternative Ranking Using TOPSIS and VIKOR: A Case Study on Social Sustainability in Agriculture," in International Conference on Decision Support System Technology, Belgium, 2016. [8] S. Nisel, "An Extended VIKOR Method for Ranking Online Graduate Business Programs," International Journal of Information and Education Technology, vol. 4, no. 1, pp. 103-107, 2014.