Abstract
To improve the decision-making process, more and more systems are being developed based on a group of multi-criteria decision analysis (MCDA) methods. Each method is based on different approaches leading to a final result. It is possible to modify the default performance of these methods, but in this case, it is worth checking whether it affects the achieved results. In this paper, the technique for order preference by similarity to an ideal solution (TOPSIS) method was used to examine the chosen distance metric’s influence to obtained results. The Euclidean and Manhattan distances were compared, while obtained rankings were compared with the similarity coefficients to check their correlation. It shows that used distance metric has an impact on the results and they are significantly different.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Behzadian, M., Otaghsara, S.K., Yazdani, M., Ignatius, J.: A state-of the-art survey of TOPSIS applications. Expert Syst. Appl. 39(17), 13051–13069 (2012)
Chiu, W.Y., Yen, G.G., Juan, T.K.: Minimum Manhattan distance approach to multiple criteria decision making in multiobjective optimization problems. IEEE Trans. Evol. Comput. 20(6), 972–985 (2016)
Danielsson, P.E.: Euclidean distance mapping. Comput. Graph. Image Process. 14(3), 227–248 (1980)
Das, B., Pal, S.C.: Assessment of groundwater vulnerability to over-exploitation using MCDA, AHP, fuzzy logic and novel ensemble models: a case study of Goghat-I and II blocks of West Bengal, India. Environ. Earth Sci. 79(5), 1–16
De Montis, A., De Toro, P., Droste-Franke, B., Omann, I., Stagl, S.: Criteria for quality assessment of MCDA methods. In: 3rd Biennial Conference of the European Society for Ecological Economics, Vienna, pp. 3–6 (2000)
Dehe, B., Bamford, D.: Development, test and comparison of two multiple criteria decision analysis (MCDA) models: a case of healthcare infrastructure location. Expert Syst. Appl. 42(19), 6717–6727 (2015)
Fabbri, R., Costa, L.D.F., Torelli, J.C., Bruno, O.M.: 2D Euclidean distance transform algorithms: a comparative survey. ACM Comput. Surv. (CSUR) 40(1), 1–44 (2008)
Gbanie, S.P., Tengbe, P.B., Momoh, J.S., Medo, J., Kabba.: Modelling landfill location using geographic information systems (GIS) and multi-criteria decision analysis (MCDA): case study Bo, Southern Sierra Leone. Appl. Geogr. 36, 3–12. V. T. S (2013)
Guitouni, A., Martel, J.M.: Tentative guidelines to help choosing an appropriate MCDA method. Eur. J. Oper. Res. 109(2), 501–521 (1998)
Harper, M., Anderson, B., James, P., Bahaj, A.: Assessing socially acceptable locations for onshore wind energy using a GIS-MCDA approach. Int. J. Low-Carbon Technol. 14(2), 160–169 (2019)
Hyde, K.M., Maier, H.R.: Distance-based and stochastic uncertainty analysis for multi-criteria decision analysis in excel using visual basic for applications. Environ. Modell. Softw. 21(12), 1695–1710 (2006)
Lavoie, T., Merlo, E.: An accurate estimation of the Levenshtein distance using metric trees and Manhattan distance. In: 2012 6th International Workshop on Software Clones (IWSC), pp. 1–7. IEEE (2012)
Mairiza, D., Zowghi, D., Gervasi, V.: Utilizing TOPSIS: a multi criteria decision analysis technique for non-functional requirements conflicts. In: Requirements Engineering, pp. 31–44. Springer, Berlin, Heidelberg (2014)
Nutt, D.J., Phillips, L.D., Balfour, D., Curran, H.V., Dockrell, M., Foulds, J., Sweanor, D.: Estimating the harms of nicotine-containing products using the MCDA approach. Eur. Add. Res. 20(5), 218–225 (2014)
Opricovic, S., Tzeng, G.H.: Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 156(2), 445–455 (2004)
Podinovski, V.V.: The quantitative importance of criteria for MCDA. J. Multi-Criteria Decis. Anal. 11(1), 1–15 (2002)
Podvezko, V.: The comparative analysis of MCDA methods SAW and COPRAS. Eng. Econ. 22(2), 134–146 (2011)
Sałabun, W., Urbaniak, K.: A new coefficient of rankings similarity in decision-making problems. In: International Conference on Computational Science, pp. 632–645. Springer, Cham (2020)
Sałabun, W., Wątrobski, J., Shekhovtsov, A.: Are MCDA methods benchmarkable? A comparative study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II methods. Symmetry 12(9), 1549 (2020)
Shekhovtsov, A., Kołodziejczyk, J.: Do distance-based multi-criteria decision analysis methods create similar rankings? Procedia Comput. Sci. 176, 3718–3729 (2020)
Shekhovtsov, A., Kołodziejczyk, J., Sałabun, W.: Fuzzy model identification using monolithic and structured approaches in decision problems with partially incomplete data. Symmetry 12(9), 1541 (2020)
Shekhovtsov, A., Sałabun, W.: A comparative case study of the VIKOR and TOPSIS rankings similarity. Procedia Comput. Sci. 176, 3730–3740 (2020)
Shekhovtsov, A., Kozlov, V., Nosov, V., Sałabun, W.: Efficiency of methods for determining the relevance of criteria in sustainable transport problems: a comparative case study. Sustainability 12(19), 7915 (2020)
Shih, H.S., Shyur, H.J., Lee, E.S.: An extension of TOPSIS for group decision making. Math. Comput. Model. 45(7–8), 801–813 (2007)
Stewart, T.J.: Dealing with uncertainties in MCDA. In: Multiple Criteria Decision Analysis: state of the Art Surveys, pp. 445–466. Springer, New York (2005)
Thokala, P., Duenas, A.: Multiple criteria decision analysis for health technology assessment. Value Health 15(8), 1172–1181 (2012)
Toledo, R.Y., Alzahrani, A.A., Martínez, L.: A food recommender system considering nutritional information and user preferences. IEEE Access 7, 96695–96711 (2019)
Urbaniak, K., Wątrobski, J., Salabun,, W.: Identification of players ranking in e-sport. Appl. Sci. 10(19), 6768 (2020)
Wątrobski, J., Sałabun, W.: Green supplier selection framework based on multi-criteria decision-analysis approach. In: International Conference on Sustainable Design and Manufacturing, pp. 361–371. Springer, Cham (2016)
Wątrobski, J., Jankowski, J.: Knowledge management in MCDA domain. In: 2015 Federated Conference on Computer Science and Information Systems (FedCSIS) (pp. 1445–1450). IEEE (2015)
Acknowledgements
The work was supported by the project financed within the framework of the program of the Minister of Science and Higher Education under the name “Regional Excellence Initiative” in the years 2019–2022, Project Number 001/RID/2018/19;the amount of financing: PLN 10.684.000,00 (J.W.).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Kizielewicz, B., Więckowski, J., Wątrobski, J. (2021). A Study of Different Distance Metrics in the TOPSIS Method. In: Czarnowski, I., Howlett, R.J., Jain, L.C. (eds) Intelligent Decision Technologies. Smart Innovation, Systems and Technologies, vol 238. Springer, Singapore. https://doi.org/10.1007/978-981-16-2765-1_23
Download citation
DOI: https://doi.org/10.1007/978-981-16-2765-1_23
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-2764-4
Online ISBN: 978-981-16-2765-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)