The comparison of Scandinavian countries’ digital society levels with a novel TOPSIS extension

Yıl 2024, Cilt: 4 Sayı: 2, 482 - 494, 31.07.2024

Furkan Göktaş

https://doi.org/10.61112/jiens.1461755

Öz

Digitalization is one of the factors that determine the future of countries. Therefore, comparing the digitalization levels of countries is an important multi-criteria decision-making (MCDM) problem. This study aims to compare the digital society levels of Scandinavian countries from an objective perspective. The main motivation of this study is to achieve this aim with a TOPSIS extension that determines criteria weights internally. Thus, a TOPSIS extension based on norm minimization (NM-TOPSIS) is proposed in this study. NM-TOPSIS determines the criteria weight vector in a way that minimizes the sum of squares of the Euclidean distances of alternatives to the negative ideal solution. In other words, it compares alternatives under the worst-case scenario. NM-TOPSIS determines the alternatives’ priority vector as the weight vector that minimizes the distance to the positive ideal solution. NM-TOPSIS depends on two different convex quadratic optimization problems. In other words, the criteria weight vector and the alternatives' priority vector are uniquely found under a certain condition. In the application made using NM-TOPSIS and current OECD data, we see that Norway's digital society level is the highest. When the same criteria weights are used, we observe that there is a high level of positive relationship between TOPSIS results and NM-TOPSIS results. On the other hand, there are significant changes in TOPSIS results depending on the change in criteria weights.

Anahtar Kelimeler

Multi-criteria decision making, Digitalization, Digital society, Convex optimization, TOPSIS

İskandinav ülkelerinin dijital toplum seviyelerinin yeni bir TOPSIS uzantısı ile karşılaştırılması

Öz

Dijitalleşme, ülkelerin geleceğini belirleyen unsurlardan biridir. Bu nedenle ülkelerin dijitalleşme düzeylerinin karşılaştırılması önemli çok kriterli karar verme (ÇKKV) problemidir. Bu çalışmanın amacı, İskandinav ülkelerinin dijital toplum seviyelerinin objektif bir bakış açısı ile karşılaştırılmasıdır. Bu çalışmanın temel motivasyonu kriter ağırlıklarını içsel olarak belirleyen bir TOPSIS uzantısı ile bu amaca ulaşmaktır. Bu nedenle norm minimizasyonuna dayalı bir TOPSIS uzantısı (NM-TOPSIS) bu çalışmada önerilmiştir. NM-TOPSIS kriterlerin ağırlık vektörünü, alternatiflerin negatif ideal çözüme olan Öklid uzaklıklarının kareleri toplamını minimize edecek şekilde belirler. Başka bir deyişle alternatifleri en kötü durum senaryosu altında karşılaştırır. NM-TOPSIS alternatiflerin öncelik vektörünü, pozitif ideal çözüme uzaklığı minimum yapan ağırlık vektörü olarak belirler. NM-TOPSIS iki farklı konveks kuadratik optimizasyon problemine dayanır. Başka bir deyişle kriterlerin ağırlık vektörü ve alternatiflerin öncelik vektörü belirli bir şart altında tek olarak bulunur. NM-TOPSIS ve güncel OECD verileri kullanılarak yapılan uygulamada, Norveç’in dijital toplum seviyesinin en yüksek olduğu görülmüştür. Aynı kriter ağırlıkları kullanıldığında, TOPSIS sonuçları ve NM-TOPSIS sonuçları arasında yüksek düzeyde pozitif yönlü ilişki olduğu görülmüştür. Öte yandan kriter ağırlıklarındaki değişime bağlı olarak TOPSIS sonuçlarında önemli değişimler vardır.

Anahtar Kelimeler

Çok kriterli karar verme, Dijitalleşme, Dijital toplum, Konveks optimizasyon, TOPSIS

Kaynakça

• OECD (2019) Going digital: Shaping policies, improving lives. OECD Publishing. https://doi.org/10.1787/9789264312012-en
• OECD (2020) OECD digital economy outlook 2020. OECD Publishing. https://doi.org/10.1787/bb167041-en
• Zerhouni MN, Özarı Ç (2022) Assessment of international digital economy and society index using entropy based TOPSIS methods. Int J Rec Res Commerce Economics Manag 9(2):70-77. https://doi.org/10.5281/zenodo.6579884
• Marti L, Puertas R (2023) Analysis of European competitiveness based on its innovative capacity and digitalization level. Technol Soc 72:102206. https://doi.org/10.1016/j.techsoc.2023.102206
• Brodny J, Tutak M (2021) Assessing the level of digitalization and robotization in the enterprises of the European Union member states. PloS One 16(7):e0254993. https://doi.org/10.1371/journal.pone.0254993
• Stankovic JJ, Marjanovic I, Drezgic S, Popovic Z (2021) The digital competitiveness of European countries: A multiple-criteria approach. J Compet 13(2):117-134. https://doi.org/10.7441/joc.2021.02.07
• Brodny J, Tutak M (2022) The level of digitization of small, medium and large enterprises in the Central and Eastern European countries and its relationship with economic parameters. J Open Innov: Technol Mark Complex 8(3):113. https://doi.org/10.3390/joitmc8030113
• Oesterreich M (2020) Dynamics of changes in the level of propensity to use the internet in European Union countries in 2010-2019. Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu 64(7):102-117. http://dx.doi.org/10.15611/pn.2020.7.08
• Małkowska A, Urbaniec M, Kosała M (2021) The impact of digital transformation on European countries: Insights from a comparative analysis. Equilib, Q J Econ Econ Policy 16(2):325-355. http://dx.doi.org/10.24136/eq.2021.012
• Banhidi Z, Dobos I (2024) Sensitivity of TOPSIS ranks to data normalization and objective weights on the example of digital development. Cent Eur J Oper Res 32(1):29-44. https://doi.org/10.1007/s10100-023-00876-y
• Banhidi Z, Dobos I (2023) A Data Envelopment Analysis model for ranking digital development in the countries of the European Union without explicit inputs and common weights analysis. Decis Anal J 6:100167. https://doi.org/10.1016/j.dajour.2023.100167
• Banhidi Z, Dobos I (2023) Measurement of digital development with partial orders, Tiered DEA, and cluster analysis for the European Union. Int Rev Appl Sci Eng 14(3):392-401. https://doi.org/10.1556/1848.2023.00612
• Georgescu MR, Lungu AE, Bogoslov IA, Stoica EA (2023) European efficiency or inefficiency in economic growth through digital transformation. Sci Ann Econ Bus 70(SI):19-31. https://doi.org/10.47743/saeb-2023-0010
• Kiselakova D, Sofrankova B, Sira E, Fedoreikova R (2022) Assessment of the digital economy's level among the EU countries-an empirical study. Pol J Manag Stud 26(1):107-123. https://doi.org/10.17512/pjms.2022.26.1.07
• Balkan D, Akyüz GA (2023) Technological maturity of the OECD countries: A multi-criteria decision-making approach using PROMETHEE. Cogent Eng 10(1):2219097. https://doi.org/10.1080/23311916.2023.2219097
• Brodny J, Tutak M (2024) Assessing the level of innovativeness and digitalization of enterprises in the European Union States. J Open Innov: Technol Mark Complex 10(1):100210. https://doi.org/10.1016/j.joitmc.2024.100210
• Pakhnenko O, Rubanov P, Hacar D, Yatsenko V, Vida I (2021) Digitalization of financial services in European countries: Evaluation and comparative analysis. J Int Stud 14(2):267-282. https://doi.org/10.14254/2071-8330.2021/14-2/17
• Brodny J, Tutak M (2022) Analyzing the level of digitalization among the enterprises of the European Union member states and their impact on economic growth. J Open Innov: Technol Mark Complex 8(2):70. https://doi.org/10.3390/joitmc8020070
• Keles EU, Alptekin GI (2023) Evaluation of the digitalization efficiency of countries using Data Envelopment Analysis. In 2023 Smart City Symposium Prague (SCSP). IEEE. https://doi.org/10.1109/SCSP58044.2023.10146126
• Bouslah K, Liern V, Ouenniche J, Pérez‐Gladish B (2023) Ranking firms based on their financial and diversity performance using multiple‐stage unweighted TOPSIS. Int Trans Oper Res 30(5):2485-2505. https://doi.org/10.1111/itor.13143
• Yıldırım Z, Sakar FM (2023) Çok kriterli karar verme yöntemlerinden TOPSIS yöntemi ile fakültelerin akademik performanslarının analizi. Dicle Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi 13(25):98-116. https://doi.org/10.53092/duiibfd.1228552
• Liern V, Pérez-Gladish B (2022) Multiple criteria ranking method based on functional proximity index: Un-weighted TOPSIS. Ann Oper Res 311(2):1099-1121. https://doi.org/10.1007/s10479-020-03718-1
• López-García A, Liern V, Pérez-Gladish B (2023) Determining the underlying role of corporate sustainability criteria in a ranking problem using UW-TOPSIS. Ann Oper Res 1-24. https://doi.org/10.1007/s10479-023-05543-8
• OECD (2024) Going digital toolkit. https://goingdigital.oecd.org/ adresinden erişildi. Erişim 15 Şubat 2024
• Acuña-Soto C, Liern V, Pérez-Gladish B (2021) Normalization in TOPSIS-based approaches with data of different nature: Application to the ranking of mathematical videos. Ann Oper Res 296(1):541-569. https://doi.org/10.1007/s10479-018-2945-5
• Liern V, Pérez-Gladish B, Rubiera-Morollón F, M’Zali B (2021) Residential choice from a multiple criteria sustainable perspective. Ann Oper Res 1-12. https://doi.org/10.1007/s10479-021-04480-8
• Trefethen LN, Bau D (1997) Numerical linear algebra. Siam.
• Grant MC, Boyd SP (2008) Graph implementations for nonsmooth convex programs. In Recent Advances in Learning and Control. Springer. https://doi.org/10.1007/978-1-84800-155-8_7
• Boyd SP, Vandenberghe L (2004) Convex optimization. Cambridge University Press.
• Li H, Cao Y, Su L (2022) Pythagorean fuzzy multi-criteria decision-making approach based on Spearman rank correlation coefficient. Soft Comput 26(6):3001-3012. https://doi.org/10.1007/s00500-021-06615-2
• Hair JF, Money AH, Samouel P, Page M (2007) Research methods for business. Education+Training 49(4): 336-337. https://doi.org/10.1108/et.2007.49.4.336.2