Dr. Bahadır Fatih Yıldırım

Özgeçmiş Akademik Blog Portfolyo Dokümanlar Kütüphane


Robust Mahalanobis Distance based TOPSIS to Evaluate the Economic Development of Provinces

Doç. Dr. Özlem Yorulmaz

İstanbul Üniversitesi Department of Econometrics, Faculty of Economics

Dr. Öğr. Üyesi Sultan Kuzu Yıldırım

İstanbul Üniversitesi Department of Quantitative Methods, School of Business

Dr. Bahadır Fatih Yıldırım

İstanbul Üniversitesi Department of Logistics, Faculty of Transportation and Logistics


In this paper, 81 Turkish provinces with different development levels were ranked using the TOPSIS method. To evaluate the ranking with TOPSIS, we presented an improvement to Mahalanobis distances, by considering a robust MM estimator of the covariance matrix to deal with the presence of outliers in the dataset. Additionally, the homogenous subsets, which were obtained from the robust Mahalanobis distance-based TOPSIS were compared with robust cluster analysis. According to our findings, robust TOPSIS-M scores reflect the inter-class differences in economic developments of provinces spanning from the extremely low to the extremely high level of economic developments. Considering indicators of economic development, which are often used in the literature, İstanbul ranked first, Ankara second, and İzmir third according to the Robust TOPSIS-M method. Moreover, with the Robust Cluster analysis, these provinces were diagnosed as outliers and it was seen that obtained clusters were compatible with the ranking of Robust TOPSIS-M.

Keywords: Economic Development, Mahalanobis Distance, Outliers, Robust Clustering, Robust TOPSIS-M

  • Ardielli, E. (2019). Use of TOPSIS method for assessing of good governance in european union countries. Review of Economic Perspectives, 19(3), 211-231. doi:10.2478/revecp-2019-0012.
  • Ardielli, E.,& Halaskova, M. (2015). Evaluation of Good Governance in EU countries. Acta academica karviniensia. 5(3), 5-17. DOI: 10.25142/aak.2015.027
  • Ascani, A., Crescenzi, R., & Iammarino, S. (2012). Regional economic development. A Review, SEARCH WP01/03, 2-26.
  • Balcerzak, A. P. & Pietrzak, M. P. (2016). Application of TOPSIS Method for Analysis of Sustainable Development in European Union Countries. In: T. Loster & T. Pavelka (Eds.). The 10th International Days of Statistics and Economics. Conference Proceedings. September 8-10, 2016. Prague, 82-92.
  • Becker, C., & Gather, U. (1999). The masking breakdown point of multivariate outlier identification rules. Journal of the American Statistical Association. 94(447), 947–955.
  • Bhutia, P. W., & Phipon, R. (2012). Appication of ahp and topsis method for supplier selection problem. IOSR Journal of Engineering. 2, 43-50.
  • Blair, John P., and Michael C. Carroll. 2008. Local economic development: analysis, practices, and globalization. 2nd ed. Los Angeles: Sage Publications.
  • Carroll, C. D., & Weil, D. N. (1994). Saving and growth: a reinterpretation. In Carnegie-Rochester conference series on public policy, North-Holland. Vol. 40, 133-192.
  • Contractor, F. J., & Mudambi, S. M. (2008). The influence of human capital investment on the exports of services and goods: An analysis of the top 25 services outsourcing countries. Management International Review, 48(4), 433-445.
  • Cooke, S., & Watson, P. (2011). A comparison of regional export enhancement and import substitution economic development strategies. Journal of Regional Analysis & Policy, 41(1), 1-15.
  • De Andrade LH, Antunes JJM, & Wanke P. (2020). Performance of TV programs: a robust MCDM approach. Benchmarking: an International Journal 27(3):1188-1209.
  • Dinçer, H., & Görener, A., (2011). Performans Değerlendirmesinde AHP-Vıkor ve AHP-TOPSIS Yaklaşımları: Hizmet Sektöründe Bir Uygulama. Sigma: Mühendislik ve Fen Bilimleri Dergisi, 29, 244-260.
  • Easterlin, R. A. (1967). Effects of population growth on the economic development of developing countries. The Annals of the American Academy of Political and Social Science, 369(1), 98-108.
  • Furuoka, F. (2009). Population growth and economic development: New empirical evidence from Thailand. Economics Bulletin, 29(1), 1-14.
  • García-Escudero, L.A., Gordaliza, A., Matrán, C. et al. (2011). Exploring the number of groups in robust model-based clustering. Stat Comput 21, 585–599. https://doi.org/10.1007/s1122…
  • García-Escudero, L.A., Gordaliza,A., Matrán, C. & Mayo-Iscar, A. (2008). A general trimming approach to robust cluster Analysis. Ann. Statist. 36 (3) 1324 -1345. https://doi.org/10.1214/07-AO…
  • Huber, P. (1981). Robust Statistics. New York: Wiley.
  • Hwang, C.L., Yoon, K., 1981. Multiple Attributes Decision Making Methods and Applications, Springer, Berlin.
  • Kaya, V., Yalçınkaya, Ö., & Hüseyni, İ. (2013). Ekonomik büyümede inşaat sektörünün rolü: Türkiye örneği (1987-2010). Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, 27(4), 148-167.
  • Kentor, J. (2001). The long term effects of globalization on income inequality, population growth, and economic development. Social Problems, 48(4), 435-455.
  • Khalif,K.M.K, Gegov, A., & Abu Bakar A.(2017). Z-TOPSIS approach for performance assessment using fuzzy similarity. 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Naples, 1-6, doi: 10.1109/FUZZ-IEEE.2017.8015458.
  • Kilic, H.S, & Yalcin A. (2020). Comparison of municipalities considering environmental sustainability via neutrosophic DEMATEL based TOPSIS. Socio-Economic Planning Sciences,2020,
  • Kizielewicz, B., Więckowski, J., Shekhovtsov, A., Wątróbski, J., Depczyński, R., & Sałabun, W. (2021). Study towards the time-based mcda ranking analysis–a supplier selection case study. Facta Universitatis, Series: Mechanical Engineering.
  • Kuncova, M., 2012. Elektronické obchodování - srovnání zemí EU v letech 2008-2009 s využitím metod vícekriteriálního hodnocení variant. In: IRCINGOVÁ, J. and J. TLUČHOŘ, Trendy v podnikání 2012. Plzeň: ZČU, 1–9. ISBN 978-80-261-0100-0.
  • Lewıs, W. Arthur (1954). Economic Development with Unlimited Supplies of Labour, The Manchester School, 22(2), 139-191.
  • Luczak, A., & Malgorzata J. (2020). The positional MEF-TOPSIS method for the assessment of complex economic phenomena in territorial units. Statistics in Transition New Series, Polish Statistical Association, 21(2), 57-172.
  • Mahalanobis P C, 1936. On the generalized distance in statistics. Proceedings of the National Institute of Sciences (Calcutta), 2: 49–55.
  • Mangır, F., & Erdogan, S. (2011).Comparison of Economic Performance Among Six Countries in Global Financial Crisis: The Application of Fuzzy TOPSIS Method. Economics, Management and Financial Markets, 6 (2), 122-136.
  • Maronna R., Martin, R. D.,& Yohai, V. (2006). Robust Statistics: Theory, Computation and Methods. New York: Wiley.
  • Mathur, V. K. (1999). Human capital-based strategy for regional economic development. Economic Development Quarterly, 13(3), 203-216.
  • Noland, M., Park, D., & Estrada, G. B. (2012). Developing the service sector as engine of growth for Asia: an overview. Asian Development Bank Economics Working Paper Series, (320).
  • Rocke, D.M., & Woodruff, D.L.(1996). Identification of outliers in multivariate data. Journal of the American Statistical Association. 91(435), 1047–1061.
  • Romm, A. T. (2002). The relationship between savings and growth in South Africa: An empirical study (Doctoral dissertation, University of the Witwatersrand).
  • Rousseeuw P., & Hubert M. (2013). High-Breakdown Estimators of Multivariate Location and Scatter. In: Becker C., Fried R., Kuhnt S. (eds) Robustness and Complex Data Structures. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3….
  • Rousseeuw, P.J, & van Zomeren,B. (1991). Robust distances: simulation and cutoff Values. In: Directions in Robust Statistics and Diagnostics, Part II. (W. Stahel, S. Weisberg, eds.), Springer-Verlag, New York.
  • Ruwet, C., García-Escudero, L.A., & Gordaliza, A. (2012). The influence function of the TCLUST robust clustering procedure. Adv Data Anal Classif, 6, 107–130.
  • Shaffer, Ron. 1989. Community economics: economic structure and change in smaller communities. 1st ed. Ames: Iowa State University Press
  • Shih,H.S., Shyur,H.J.,& Lee, E.S. (2007). An extension of TOPSIS for group decision making,Mathematical and Computer Modelling,45, (7–8), 801-813.
  • Srinivasan, T. N. (1988). Population growth and economic development. Journal of Policy Modeling, 10(1), 7-28.
  • Vavrek, R., Becica, J., Papcunova, V., Gundova, P.,& Mitríková, J.(2021). Number of Financial Indicators as a Factor of Multi-Criteria Analysis via the TOPSIS Technique: A Municipal Case Study. Algorithms, 14, 64. https://doi.org/10.3390/a1402…
  • Vavrek,R., Kotulic,R,& Adamisin, P. (2015) Evaluation of municipalities management with the topsis technique emphasising on the impact of weights of established criteria, Lex Localis, 13 (2), 249
  • Wang, Y.-M., & Elhag, T. M. S. (2006). Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert Systems with Applications, 31(2), 309–319. doi:10.1016/j.eswa.2005.09.040
  • Wang, Z.-X., & Wang, Y.-Y. (2014). Evaluation of the provincial competitiveness of the Chinese high-tech industry using an improved TOPSIS method. Expert Systems with Applications, 41(6), 2824–2831. doi:10.1016/j.eswa.2013.10.015
  • Xiang, S., Nie, F., & Zhang, C. (2008). Learning a Mahalanobis distance metric for data clustering and classification. Pattern Recognition, 41(12), 3600–3612. doi:10.1016/j.patcog.2008.05.018
  • Yoon, K. P., & Hwang, C.-L. (1995). Quantitative applications in the social sciences, No. 07-104.Multiple attribute decision making: An introduction. Sage university papers series. Sage Publications, Inc.
  • Özsağır, A., & Akın, A. (2012). Hizmetler Sektörü İçinde Hizmet Ticaretinin Yeri Ve Karşilaştirmali Bir Analizi. Elektronik Sosyal Bilimler Dergisi, 11(41), 311-331.
  • Makale
    Ismael, S. F., Alias, A. H., Zaidan, A. A., Zaidan, B. B., Alsattar, H. A., Qahtan, S., Albahri, O. S., Talal, M., Alamoodi, A. H., & Mohammed, R. T. (2023). Toward Sustainable Transportation: A Pavement Strategy Selection Based on the Extension of Dual-Hesitant Fuzzy Multicriteria Decision-Making Methods. IEEE Transactions on Fuzzy Systems, 31(2), 380–393. doi: 10.1109/tfuzz.2022.3168050
  • Mahmood, S., Amin, M., Baig Mirza, M., Abu-Ghumsan, S., Akram, M., Mahmood Janjua, Z., Shahid, A., & Shahid, U. (2023). Multi Criteria Decision Making for Evaluation and Ranking of Cancer Information. In Computers, Materials & Continua (Vol. 74, Issue 2, pp. 4469–4481). Computers, Materials and Continua (Tech Science Press). doi:10.32604/cmc.2023.030728
  • Pamucar, D., Görçün, Ö. F., & Küçükönder, H. (2022). Evaluation of the route selection in international freight transportation by using the CODAS technique based on interval-valued Atanassov intuitionistic sets. Soft Computing. doi: 10.1007/s00500-022-07707-3
  • Makale
    Tutak, M., & Brodny, J. (2022). Evaluating differences in the Level of Working Conditions between the European Union Member States using TOPSIS method. Decision Making: Applications in Management and Engineering, 5(2), 1-29. DOI: 10.31181/dmame0305102022t
  • Makale
    Xiong, Y. (2022). Operational efficiency evaluation of urban and rural residents' basic pension insurance system by utilizing a picture fuzzy TOPSIS method based on the cumulative prospect theory. Frontiers in Public Health, 10, 1009207. doi: 10.3389/fpubh.2022.1009207
  • Makale
    Zhang, Z.-X., Wang, L., & Wang, Y.-M. (2022). A Novel Early Warning Method for Handling Non-Homogeneous Information. Mathematics, 10(16), 3016. DOI: 10.3390/math10163016
  • Sindhu, M. S., Siddique, I., Ahsan, M., Jarad, F., & Altunok, T. (2022). An Approach of Decision-Making under the Framework of Fermatean Fuzzy Sets. Mathematical Problems in Engineering, 2022, 1–9. doi:10.1155/2022/8442123
  • Erdogan, M., & Ayyildiz, E. (2022). Comparison of hospital service performances under COVID-19 pandemics for pilot regions with low vaccination rates. Expert Systems with Applications, 117773. doi:10.1016/j.eswa.2022.117773
  • Zhang, Z., & Su, P. (2022). Research on the English Classroom Teaching Effect Evaluation with Interval-Valued Intuitionistic Fuzzy Grey Relational Analysis Method. Mathematical Problems in Engineering, 2022, 1–11. doi:10.1155/2022/7445250
  • Makale
    Correa da Cunha, H., Singh, V., & Xie, S. (2022). The Determinants of Outward Foreign Direct Investment from Latin America and the Caribbean: An Integrated Entropy-Based TOPSIS Multiple Regression Analysis Framework. Journal of Risk and Financial Management, 15(3), 130. doi: 10.3390/jrfm15030130
  • Riaz, M., Pamucar, D., Habib, A., & Riaz, M. (2021). A New TOPSIS Approach Using Cosine Similarity Measures and Cubic Bipolar Fuzzy Information for Sustainable Plastic Recycling Process", Mathematical Problems in Engineering, vol. 2021, Article ID 4309544, 18 pages, 2021. doi: 10.1155/2021/4309544
  • Makale
    Saeed, M., Mehmood, A. & Arslan, M. (2021). Multipolar Interval-Valued Fuzzy Set with Application of Similarity Measures and multi-person TOPSIS technique. Punjab University Journal of Mathematics, 53 (10), 691-710. doi.10.52280/pujm.2021.531001
  • Hashmi, M. R., Tehrim, S. T., Riaz, M., Pamucar, D., & Cirovic, G. (2021). Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making. Axioms, 10(3), 185. doi:10.3390/axioms10030185
  • Yorulmaz, Ö., Kuzu Yıldırım, S. & Yıldırım, B. F. (). Robust Mahalanobis Distance based TOPSIS to Evaluate the Economic Development of Provinces. Operational Research in Engineering Sciences: Theory and Applications, 4(2), 102-123. https://doi.org/10.31181/oresta20402102y