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APPLICATION OF THE PIV METHOD IN THE PRESENCE OF NEGATIVE DATA: AN EMPIRICAL EXAMPLE FROM A REAL-WORLD CASE

Yıl 2021, , 318 - 337, 31.12.2021
https://doi.org/10.17218/hititsbd.974522

Öz

The presence of negative data in the decision matrix is a rare situation in Multiple Criteria Decision Making (MCDM) methods. In such a case, normalized matrix elements must be between 0 and 1 to adopt the Proximity Indexed Value (PIV) method. In this study, which deals with real life application, two different solutions are presented to find a solution to this problem. Firstly, negative decision matrix elements are converted to positive using a z-score standardization method. Secondly, different normalization techniques are used instead of vector normalization in the algorithm of the PIV method. According to the results obtained, the most appropriate technique to reach a result with the PIV method in the presence of negative data is the min-max technique. The model proposed in this study supports the usage the PIV method in the presence of negative data. In addition, this study is the first to test the suitability of different techniques for the PIV method.

Kaynakça

  • Abdel-Basset, M., Ding, W., Mohamed, R. and Metawa, N. (2020). An integrated plithogenic MCDM approach for financial performance evaluation of manufacturing industries. Risk Management, 22 (3), 192-218.doi:10.1057/s41283-020-00061-4
  • Asgharpour, M. J. (1998). Multiple criteria decision making. Tehran: Tehran University Press.
  • Bland, J. M. and Altman, D.G. (1996). Statistics notes: Measurement error. BMJ, 313(7059), 744-744. doi: 10.1136/bmj.313.7059.744
  • Celen, A. (2014). Comparative analysis of normalization procedures in TOPSIS method: with an application to Turkish deposit banking market. Informatica, 25(2), 185-208. Doi: 10.15388/Informatica.2014.10
  • Chakraborty, S. and Yeh, C. H. (2007). A simulation based comparative study of normalization procedures in multiattribute decision making. In Proceedings of the 6th Conference on 6th WSEAS Int. Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (pp. 102-109). Wisconsin, USA.
  • Chakraborty, S. and Yeh, C. H. (2009). A simulation comparison of normalization procedures for TOPSIS. In 2009 International Conference on Computers & Industrial Engineering (pp. 1815-1820). France.
  • Chatterjee, P.; Chakraborty, S. (2014). Investigating the Effect of Normalization Norms in Flexible Manufacturing Sytem Selection Using Multi-Criteria Decision-Making Methods. Journal of Engineering Science & Technology Review, 7(3), 141-150. Doi:10.25103/jestr.073.23
  • d’Angelo, A., Eskandari, A. and Szidarovszky, F. (1998). Social choice procedures in water resource management. Journal of Environmental Management, 52(3), 203–210. doi: 10.1006/jema.1997.0156
  • Dinçer, H. and Yüksel, S. (2018). Comparative evaluation of BSC-based new service development competencies in Turkish banking sector with the integrated fuzzy hybrid MCDM using content analysis. International Journal of Fuzzy Systems, 20(8), 2497-2516. doi: 10.1007/s40815-018-0519-y
  • Ehrgott, M., Klamroth, K. and Schwehm, C. (2004). An MCDM approach to portfolio optimization. European Journal of Operational Research, 155(3), 752-770. doi: 10.1016/S0377-2217(02)00881-0
  • Farag, M. M. (1997). Materials selection for engineering design. USA: Prentice Hall.
  • Ghadikolaei, S. A., Esbouei, K. S. and Antucheviciene, J. (2014). Applying fuzzy MCDM for financial performance evaluation of Iranian companies. Technological and Economic Development of Economy, 20(2), 274-291. doi: 10.3846/20294913.2014.913274
  • Guo, Q. (2004). Minkowski Measure of Asymmetry and Minkowski Distance for Convex Bodies. Doctoral Dissertation. Uppsala University Department of Mathematics, Uppsala.
  • Hassan, D., Aickelin, U. and Wagner, C. (2014). Comparison of distance metrics for hierarchical data in medical databases. International Joint Conference on Neural Networks (pp. 3636-3643). Beijing, China.
  • Jahan, A. and Edwards, K.L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: improving the materials selection process in engineering design. Materials & Design, 65, 335–342. doi: 10.1016/j.matdes.2014.09.022
  • Jahan, A., Mustapha, F., Sapuan, S. M., Ismail, M. Y. and Bahraminasab, M. (2012). A Framework for Weighting of Criteriain Ranking Stage of Material Selection Process. The International Journal of Advanced Manufacturing Technology, 58(1), 411-420. doi: 10.1007/s00170-011-3366-7
  • Jüttler, H. (1966). Untersuchungen zur Fragen der Operationsforschung und ihrer Anwendungsmöglichkeiten auf ökonomische Problemstellungen unter besonderer Berücksichtigung der Spieltheorie. Dissertation A an der Wirtschaftswissenschaftlichen Fakultät der Humboldt-Universität Berlin.
  • Kosareva, N., Krylovas, A. and Zavadskas, E. K. (2018). Statistical analysis of MCDM data normalization methods using Monte Carlo approach: The case of ternary estimates matrix. Economic Computation and Economic Cybernetics Studies and Research, 52, 159-175. doi: 10.24818/18423264/52.4.18.11
  • Körth, H. (1969). Zur Berücksichtigung mehrer Zielfunktionen bei der Optimierung von Produktionsplanen. Mathematik und Wirtschaft, 6, 184–201.
  • Kumar, A., Sah, B., Singh, A. R., Deng, Y., He, X., Kumar, P. and Bansal, R. C. (2017). A review of multi criteria decision making (MCDM) towards sustainable renewable energy development. Renewable and Sustainable Energy Reviews, 69, 596-609. doi: 10.1016/j.rser.2016.11.191
  • Lai, Y.J. and Hwang, C.L. (1994). Fuzzy Multiple Objective Decision Making: Methods and Applications. Berlin: Springer.
  • Markovic, Z. (2010). Modification of TOPSIS method for solving of multicriteria tasks. The Yugoslav Journal of Operations Research, 20(1), 117-143. doi: 10.2298/YJOR1001117M
  • Mathew, M., Sahu, S. and Upadhyay, A. K. (2017). Effect of normalization techniques in robot selection using weighted aggregated sum product assessment. Int. J. Innov. Res. Adv. Stud, 4(2), 59-63. Retrieved from: https://www.ijiras.com/2017/Vol_4-Issue_2/paper_12.pdf
  • Matić, B., Jovanović, S., Das, D. K., Zavadskas, E. K., Stević, Ž., Sremac, S. and Marinković, M. (2019). A new hybrid MCDM model: Sustainable supplier selection in a construction company. Symmetry, 11(3), 1-24. doi: 10.3390/sym11030353
  • Milani, A. S., Shanian, A., Madoliat, R. and Nemes, J. A. (2005). The effect of normalization norms in multiple attribute decision making models: a case study in gear material selection. Structural and multidisciplinary optimization, 29(4), 312-318. doi: 10.1007/s00158-004-0473-1
  • Mousavi-Nasab, S. H. and Sotoudeh-Anvari, A. (2017). A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems. Materials & Design, 121, 237-253. doi: 10.1016/j.matdes.2017.02.041
  • Mufazzal, S. and Muzakkir, S. M. (2018). A new multi-criterion decision making (MCDM) method based on proximity indexed value for minimizing rank reversals. Computers & Industrial Engineering, 119, 427-438. doi: 10.1016/j.cie.2018.03.045
  • Peldschus, F. (1986). Zur Anwendung der Theorie der Spiele für Aufgaben der Bautechnologie. Dissertation B, Technische Hochschule Leipzig.
  • Pineda, P. J. G., Liou, J. J., Hsu, C. C. and Chuang, Y. C. (2018). An integrated MCDM model for improving airline operational and financial performance. Journal of Air Transport Management, 68, 103-117. doi: 10.1016/j.jairtraman.2017.06.003
  • Shyur, H. J. and Shih, H. S. (2006). A hybrid MCDM model for strategic vendor selection. Mathematical and computer modelling, 44(7-8), 749-761. doi: 10.1016/j.mcm.2005.04.018
  • Stević, Ž., Pamučar, D., Puška, A. and Chatterjee, P. (2020). Sustainable supplier selection in healthcare industries using a new MCDM method: Measurement of alternatives and ranking according to COmpromise solution (MARCOS). Computers & Industrial Engineering, 140, 1-15. doi: 10.1016/j.cie.2019.106231
  • Stopp, F. (1975). Variantenvergleich durch Matrixspiele, Wissenschaftliche Zeitschrift der Hochschule für Bauwesen Leipzig, Heft 2.
  • Tzeng, G. H. and Huang, J. J. (2011). Multiple attribute decision making: methods and applications, Florida, ABD: CRC Press.
  • Vafaei, N., Ribeiro, R. A. and Camarinha-Matos, L. M. (2016). Normalization techniques for multi-criteria decision making: analytical hierarchy process case study. In doctoral conference on computing, electrical and industrial systems (pp. 261-269). Springer, Cham.
  • Vafaei, N., Ribeiro, R. A. and Camarinha-Matos, L. M. (2018). Data normalisation techniques in decision making: case study with TOPSIS method. International journal of information and decision sciences, 10(1), 19-38. doi: 10.1504/IJIDS.2018.090667
  • Vafaei, N., Ribeiro, R. A. and Camarinha-Matos, L. M. (2020). Selecting Normalization Techniques for the Analytical Hierarchy Process. In Doctoral Conference on Computing, Electrical and Industrial Systems (pp. 43-52). Springer, Cham.
  • Vafaei, N., Ribeiro, R. A., Camarinha-Matos, L. M. and Valera, L. R. (2019). Normalization techniques for collaborative networks. Kybernetes, 49(4), 1285-1304. doi: 10.1108/K-09-2018-0476
  • Wang, Y. M. and Luo, Y. (2010). Integration of Correlations with Standard Deviations for Determining Attribute Weights in Multiple Attribute Decision Making. Mathematical and Computer Modelling, 51(1-2), 1-12. doi: 10.1016/j.mcm.2009.07.016
  • Weitendorf, D. (1976). Beitrag zur Optimierung der räumlichen Struktur eines Gebäudes, Dissertation A. Hochschule für Architektur und Bauwesen. Weimar.
  • Yazdani, M., Chatterjee, P., Zavadskas, E. K. and Zolfani, S. H. (2017b). Integrated QFD-MCDM framework for green supplier selection. Journal of Cleaner Production, 142, 3728-3740. doi: 10.1016/j.jclepro.2016.10.095
  • Yazdani, M., Jahan, A. and Zavadskas, E. (2017a). Analysis in Material Selection: Influence of Normalization Tools on Copras-G. Economic Computation & Economic Cybernetics Studies & Research, 51(1), 59-74. Retrieved from: http://www.ipe.ro/RePEc/cys/ecocyb_pdf/ecocyb1_2017p59-74.pdf
  • Yeh, C. H. (2003). The selection of multiattribute decision making methods for scholarship student selection. International Journal of Selection and Assessment, 11(4), 289-296. doi: 10.1111/j.0965-075X.2003.00252.x
  • Zavadskas, E. K. and Turskis, Z. (2008). A new logarithmic normalization method in games theory. Informatica, 19(2), 303-314. doi: 10.15388/Informatica.2008.215
  • Zhang, X., Wang, C., Li, E. and Xu, C. (2014). Assessment Model of Eco-environmental Vulnerability Based on Improved Entropy Weight Method. The Scientific World Journal, 2014, 1-7. doi: 10.1155/2014/797814

NEGATİF VERİLERİN VARLIĞI DURUMUNDA PIV YÖNTEMİNİN UYGULANMASI: GERÇEK HAYAT UYGULAMASINA DAYALI AMPİRİK BİR ANALİZ

Yıl 2021, , 318 - 337, 31.12.2021
https://doi.org/10.17218/hititsbd.974522

Öz

Çok Kriterli Karar Verme (ÇKKV) yöntemlerinde karar matrisinde negatif verilere nadir olarak rastlanılmaktadır. Böyle bir durumda Proximity Indexed Value- Yakınlık Endeksli Değer (PIV) yöntemini uygulamak için normalize edilmiş karar matrisi elemanlarının 0 ile 1 arasında olacak şekilde yeniden düzenlenmesi gerekmektedir. Gerçek hayat uygulamasının ele alındığı bu çalışmada, mevcut problemi ortadan kaldırmak amacıyla iki farklı çözüm yolu sunulmuştur. İlk olarak, negatif karar matrisi elemanları, z-skor standardizasyon yöntemi kullanılarak pozitif hale getirilmiştir. İkinci olarak, PIV yönteminin algoritmasında bulunan vektör normalizasyon tekniği yerine farklı normalizasyon teknikleri kullanılmıştır. Elde edilen sonuçlara göre karar matrisinde negatif verilerin varlığı durumunda PIV yöntemi ile sonuca ulaşmak için en uygun teknik min-max tekniğidir. Bu çalışmada önerilen model, karar matrisinde negatif verilerin bulunması durumunda PIV yönteminin kullanımını desteklemektedir. Ayrıca, bu çalışma farklı tekniklerin PIV yöntemi için uygunluğunu test eden ilk çalışmadır.

Kaynakça

  • Abdel-Basset, M., Ding, W., Mohamed, R. and Metawa, N. (2020). An integrated plithogenic MCDM approach for financial performance evaluation of manufacturing industries. Risk Management, 22 (3), 192-218.doi:10.1057/s41283-020-00061-4
  • Asgharpour, M. J. (1998). Multiple criteria decision making. Tehran: Tehran University Press.
  • Bland, J. M. and Altman, D.G. (1996). Statistics notes: Measurement error. BMJ, 313(7059), 744-744. doi: 10.1136/bmj.313.7059.744
  • Celen, A. (2014). Comparative analysis of normalization procedures in TOPSIS method: with an application to Turkish deposit banking market. Informatica, 25(2), 185-208. Doi: 10.15388/Informatica.2014.10
  • Chakraborty, S. and Yeh, C. H. (2007). A simulation based comparative study of normalization procedures in multiattribute decision making. In Proceedings of the 6th Conference on 6th WSEAS Int. Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (pp. 102-109). Wisconsin, USA.
  • Chakraborty, S. and Yeh, C. H. (2009). A simulation comparison of normalization procedures for TOPSIS. In 2009 International Conference on Computers & Industrial Engineering (pp. 1815-1820). France.
  • Chatterjee, P.; Chakraborty, S. (2014). Investigating the Effect of Normalization Norms in Flexible Manufacturing Sytem Selection Using Multi-Criteria Decision-Making Methods. Journal of Engineering Science & Technology Review, 7(3), 141-150. Doi:10.25103/jestr.073.23
  • d’Angelo, A., Eskandari, A. and Szidarovszky, F. (1998). Social choice procedures in water resource management. Journal of Environmental Management, 52(3), 203–210. doi: 10.1006/jema.1997.0156
  • Dinçer, H. and Yüksel, S. (2018). Comparative evaluation of BSC-based new service development competencies in Turkish banking sector with the integrated fuzzy hybrid MCDM using content analysis. International Journal of Fuzzy Systems, 20(8), 2497-2516. doi: 10.1007/s40815-018-0519-y
  • Ehrgott, M., Klamroth, K. and Schwehm, C. (2004). An MCDM approach to portfolio optimization. European Journal of Operational Research, 155(3), 752-770. doi: 10.1016/S0377-2217(02)00881-0
  • Farag, M. M. (1997). Materials selection for engineering design. USA: Prentice Hall.
  • Ghadikolaei, S. A., Esbouei, K. S. and Antucheviciene, J. (2014). Applying fuzzy MCDM for financial performance evaluation of Iranian companies. Technological and Economic Development of Economy, 20(2), 274-291. doi: 10.3846/20294913.2014.913274
  • Guo, Q. (2004). Minkowski Measure of Asymmetry and Minkowski Distance for Convex Bodies. Doctoral Dissertation. Uppsala University Department of Mathematics, Uppsala.
  • Hassan, D., Aickelin, U. and Wagner, C. (2014). Comparison of distance metrics for hierarchical data in medical databases. International Joint Conference on Neural Networks (pp. 3636-3643). Beijing, China.
  • Jahan, A. and Edwards, K.L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: improving the materials selection process in engineering design. Materials & Design, 65, 335–342. doi: 10.1016/j.matdes.2014.09.022
  • Jahan, A., Mustapha, F., Sapuan, S. M., Ismail, M. Y. and Bahraminasab, M. (2012). A Framework for Weighting of Criteriain Ranking Stage of Material Selection Process. The International Journal of Advanced Manufacturing Technology, 58(1), 411-420. doi: 10.1007/s00170-011-3366-7
  • Jüttler, H. (1966). Untersuchungen zur Fragen der Operationsforschung und ihrer Anwendungsmöglichkeiten auf ökonomische Problemstellungen unter besonderer Berücksichtigung der Spieltheorie. Dissertation A an der Wirtschaftswissenschaftlichen Fakultät der Humboldt-Universität Berlin.
  • Kosareva, N., Krylovas, A. and Zavadskas, E. K. (2018). Statistical analysis of MCDM data normalization methods using Monte Carlo approach: The case of ternary estimates matrix. Economic Computation and Economic Cybernetics Studies and Research, 52, 159-175. doi: 10.24818/18423264/52.4.18.11
  • Körth, H. (1969). Zur Berücksichtigung mehrer Zielfunktionen bei der Optimierung von Produktionsplanen. Mathematik und Wirtschaft, 6, 184–201.
  • Kumar, A., Sah, B., Singh, A. R., Deng, Y., He, X., Kumar, P. and Bansal, R. C. (2017). A review of multi criteria decision making (MCDM) towards sustainable renewable energy development. Renewable and Sustainable Energy Reviews, 69, 596-609. doi: 10.1016/j.rser.2016.11.191
  • Lai, Y.J. and Hwang, C.L. (1994). Fuzzy Multiple Objective Decision Making: Methods and Applications. Berlin: Springer.
  • Markovic, Z. (2010). Modification of TOPSIS method for solving of multicriteria tasks. The Yugoslav Journal of Operations Research, 20(1), 117-143. doi: 10.2298/YJOR1001117M
  • Mathew, M., Sahu, S. and Upadhyay, A. K. (2017). Effect of normalization techniques in robot selection using weighted aggregated sum product assessment. Int. J. Innov. Res. Adv. Stud, 4(2), 59-63. Retrieved from: https://www.ijiras.com/2017/Vol_4-Issue_2/paper_12.pdf
  • Matić, B., Jovanović, S., Das, D. K., Zavadskas, E. K., Stević, Ž., Sremac, S. and Marinković, M. (2019). A new hybrid MCDM model: Sustainable supplier selection in a construction company. Symmetry, 11(3), 1-24. doi: 10.3390/sym11030353
  • Milani, A. S., Shanian, A., Madoliat, R. and Nemes, J. A. (2005). The effect of normalization norms in multiple attribute decision making models: a case study in gear material selection. Structural and multidisciplinary optimization, 29(4), 312-318. doi: 10.1007/s00158-004-0473-1
  • Mousavi-Nasab, S. H. and Sotoudeh-Anvari, A. (2017). A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems. Materials & Design, 121, 237-253. doi: 10.1016/j.matdes.2017.02.041
  • Mufazzal, S. and Muzakkir, S. M. (2018). A new multi-criterion decision making (MCDM) method based on proximity indexed value for minimizing rank reversals. Computers & Industrial Engineering, 119, 427-438. doi: 10.1016/j.cie.2018.03.045
  • Peldschus, F. (1986). Zur Anwendung der Theorie der Spiele für Aufgaben der Bautechnologie. Dissertation B, Technische Hochschule Leipzig.
  • Pineda, P. J. G., Liou, J. J., Hsu, C. C. and Chuang, Y. C. (2018). An integrated MCDM model for improving airline operational and financial performance. Journal of Air Transport Management, 68, 103-117. doi: 10.1016/j.jairtraman.2017.06.003
  • Shyur, H. J. and Shih, H. S. (2006). A hybrid MCDM model for strategic vendor selection. Mathematical and computer modelling, 44(7-8), 749-761. doi: 10.1016/j.mcm.2005.04.018
  • Stević, Ž., Pamučar, D., Puška, A. and Chatterjee, P. (2020). Sustainable supplier selection in healthcare industries using a new MCDM method: Measurement of alternatives and ranking according to COmpromise solution (MARCOS). Computers & Industrial Engineering, 140, 1-15. doi: 10.1016/j.cie.2019.106231
  • Stopp, F. (1975). Variantenvergleich durch Matrixspiele, Wissenschaftliche Zeitschrift der Hochschule für Bauwesen Leipzig, Heft 2.
  • Tzeng, G. H. and Huang, J. J. (2011). Multiple attribute decision making: methods and applications, Florida, ABD: CRC Press.
  • Vafaei, N., Ribeiro, R. A. and Camarinha-Matos, L. M. (2016). Normalization techniques for multi-criteria decision making: analytical hierarchy process case study. In doctoral conference on computing, electrical and industrial systems (pp. 261-269). Springer, Cham.
  • Vafaei, N., Ribeiro, R. A. and Camarinha-Matos, L. M. (2018). Data normalisation techniques in decision making: case study with TOPSIS method. International journal of information and decision sciences, 10(1), 19-38. doi: 10.1504/IJIDS.2018.090667
  • Vafaei, N., Ribeiro, R. A. and Camarinha-Matos, L. M. (2020). Selecting Normalization Techniques for the Analytical Hierarchy Process. In Doctoral Conference on Computing, Electrical and Industrial Systems (pp. 43-52). Springer, Cham.
  • Vafaei, N., Ribeiro, R. A., Camarinha-Matos, L. M. and Valera, L. R. (2019). Normalization techniques for collaborative networks. Kybernetes, 49(4), 1285-1304. doi: 10.1108/K-09-2018-0476
  • Wang, Y. M. and Luo, Y. (2010). Integration of Correlations with Standard Deviations for Determining Attribute Weights in Multiple Attribute Decision Making. Mathematical and Computer Modelling, 51(1-2), 1-12. doi: 10.1016/j.mcm.2009.07.016
  • Weitendorf, D. (1976). Beitrag zur Optimierung der räumlichen Struktur eines Gebäudes, Dissertation A. Hochschule für Architektur und Bauwesen. Weimar.
  • Yazdani, M., Chatterjee, P., Zavadskas, E. K. and Zolfani, S. H. (2017b). Integrated QFD-MCDM framework for green supplier selection. Journal of Cleaner Production, 142, 3728-3740. doi: 10.1016/j.jclepro.2016.10.095
  • Yazdani, M., Jahan, A. and Zavadskas, E. (2017a). Analysis in Material Selection: Influence of Normalization Tools on Copras-G. Economic Computation & Economic Cybernetics Studies & Research, 51(1), 59-74. Retrieved from: http://www.ipe.ro/RePEc/cys/ecocyb_pdf/ecocyb1_2017p59-74.pdf
  • Yeh, C. H. (2003). The selection of multiattribute decision making methods for scholarship student selection. International Journal of Selection and Assessment, 11(4), 289-296. doi: 10.1111/j.0965-075X.2003.00252.x
  • Zavadskas, E. K. and Turskis, Z. (2008). A new logarithmic normalization method in games theory. Informatica, 19(2), 303-314. doi: 10.15388/Informatica.2008.215
  • Zhang, X., Wang, C., Li, E. and Xu, C. (2014). Assessment Model of Eco-environmental Vulnerability Based on Improved Entropy Weight Method. The Scientific World Journal, 2014, 1-7. doi: 10.1155/2014/797814
Toplam 44 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Nazlı Ersoy 0000-0003-0011-2216

Yayımlanma Tarihi 31 Aralık 2021
Gönderilme Tarihi 26 Temmuz 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Ersoy, N. (2021). APPLICATION OF THE PIV METHOD IN THE PRESENCE OF NEGATIVE DATA: AN EMPIRICAL EXAMPLE FROM A REAL-WORLD CASE. Hitit Sosyal Bilimler Dergisi, 14(2), 318-337. https://doi.org/10.17218/hititsbd.974522
                                                     Hitit Sosyal Bilimler Dergisi  Creative Commons Atıf-GayriTicari 4.0 Uluslararası Lisansı (CC BY NC) ile lisanslanmıştır.