Sarfaraz Hashemkhani Zolfani, Morteza Yazdani, Dragan Pamucar, Pascale Zarate

DOI Number
First page
Last page


Decision and policy-makers in multi-criteria decision-making analysis take into account some strategies in order to analyze outcomes and to finally make an effective and more precise decision. Among those strategies, the modification of the normalization process in the multiple-criteria decision-making algorithm is still a question due to the confrontation of many normalization tools. Normalization is the basic action in defining and solving a MADM problem and a MADM model. Normalization is the first, also necessary, step in solving, i.e. the application of a MADM method.  It is a fact that the selection of normalization methods has a direct effect on the results. One of the latest normalization methods introduced is the Logarithmic Normalization (LN) method. This new method has a distinguished advantage, reflecting in that a sum of the normalized values of criteria always equals 1. This normalization method had never been applied in any MADM methods before. This research study is focused on the analysis of the classical MADM methods based on logarithmic normalization. VIKOR and TOPSIS, as the two famous MADM methods, were selected for this reanalysis research study. Two numerical examples were checked in both methods, based on both the classical and the novel ways based on the LN. The results indicate that there are differences between the two approaches. Eventually, a sensitivity analysis is also designed to illustrate the reliability of the final results.


Multiple attributes decision-making, MADM, Normalization, Logarithmic normalization, VIKOR, TOPSIS

Full Text:



Jassbi, J.J., Ribeiro, R.A., Varela, L.R., 2014, Dynamic MCDM with future knowledge for supplier selection, Journal of Decision Systems, 23(3), pp. 232-248.

Zavadskas, E.K., Zakarevicius, A., Antucheviciene, J., 2006, Evaluation of ranking accuracy in multi-criteria decisions, Informatica, 17(4), pp. 601-618.

Chen, T., 2011, Using hybrid MCDM model for enhancing the participation of teacher in recreational sports, Journal of Decision Systems, 20(1), pp. 33-49.

Köksalan, M., Wallenius, J., Zionts, S., 2013, An early history of multiple criteria decision making. Journal of Multi‐Criteria Decision Analysis, 20(1-2), pp. 87-94.

Ignatius, J., Rahman, A., Yazdani, M., Šaparauskas, J., Haron, S.H., 2016, An integrated fuzzy ANP–QFD approach for green building assessment, Journal of Civil Engineering and Management, 22(4), pp. 551-563.

Chatterjee, P., Chakraborty, S., 2014, Investigating the effect of normalization norms in flexible manufacturing system selection using multi criteria decision making methods, Journal of engineering science and technology review, 7(3), pp. 141-150.

Zavadskas, E. K., Turskis, Z., 2008, A new logarithmic normalization method in games theory, Informatica, 19(2), pp. 303-314.

Eftekhary, M., Gholami, P., Safari, S., Shojaee, M., 2012, ranking normalization methods for improving the accuracy of SVM algorithm by DEA method, Modern applied science, 6(10), pp. 26-36.

Peldschus, F., Vaigauskas, E., Zavadskas, E.K., 1983, Technologische entscheidungen bei der berücksichtigung mehrerer Ziehle.

Vafaei, N., Ribeiro, R.A., 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), pp. 19-38.

Zadeh Sarraf, A., Mohaghar, A., Bazargani, H., 2013, Developing TOPSIS method using statistical normalization for selecting Knowledge management strategies, Journal of industrial engineering and management, 6(4), pp. 860-875.

Álvarez Carrillo, P.A., Leyva López, J.C., Sánchez Castañeda, M.D.L.D., 2015, An empirical study of the consequences of coordination modes on supporting multicriteria group decision aid methodologies, Journal of decision systems, 24(4), pp. 383-405.

Lai, Y.J., Liu, T.Y., Hwang, C.L., 1994, TOPSIS for MODM, European journal of operational research, 76(3), pp. 486-500.

Mareschal, B., Mertens, D., 1992, Banks a multicriteria, PROMETHEE-based, decision support system for the evaluation of the international banking sector, Journal of decision systems, 1(2-3), pp. 175-189.

Behzadian, M., Kazemzadeh, R.B., Albadvi, A., Aghdasi, M., 2010, PROMETHEE: A comprehensive literature review on methodologies and applications, European journal of operational research, 200(1), pp. 198-215.

Opricovic, S., Tzeng, G.H., 2003, Fuzzy multi-criteria model for post-earthquake land-use planning, Natural hazards review, 4(2), 59-64.

Opricovic, S., Tzeng, G.H., 2004, Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, European journal of operational research, 156(2), pp. 445-455.

Wang, P., Zhu, Z., Wang, Y., 2016, A novel hybrid MCDM model combining the SAW, TOPSIS and GRA methods based on experimental design, Information Sciences, 345, pp. 27-45.

Omar, M.N., Fayek, A.R., 2016, A TOPSIS-based approach for prioritized aggregation in multi-criteria decision-making problems, Journal of multi-criteria decision analysis, doi: 10.1002/mcda.1561.

Opricovic, S., 1998, Multi-criteria optimization of civil engineering systems, Faculty of Civil Engineering, Belgrade, 2(1), pp. 5-21.

Yazdani, M., Graeml, F.R., 2014, VIKOR and its applications: A state-of-the-art survey, International Journal of Strategic Decision Sciences, 5(2), 56-83.

Noureddine, M., Ristic, M., 2019, Route planning for hazardous materials transportation: Multicriteria decision making approach, Decision making: applications in management and engineering, 2(1), pp. 66-85.

Bozanic, D., Tešić, D., Kočić, J., 2019, Multi-criteria FUCOM – Fuzzy MABAC model for the selection of location for construction of single-span bailey bridge, Decision making: applications in management and engineering, 2(1), pp. 132-146.

Nunić, Z., 2018, Evaluation and selection of Manufacturer PVC carpentry using FUCOM-MABAC model, Operational research in engineering sciences: Theory and applications, 1(1), pp. 13-28.

Erceg, Ž., Mularifović, F., 2019, Integrated MCDM model for processes optimization in supply chain management in wood company, Operational research in engineering sciences: Theory and applications, 2(1), pp. 37-50.

Opricovic, S., 2009, A compromise solution in water resources planning, Water resources management, 23(8), pp. 1549-1561.

Opricovic, S., Tzeng, G.H., 2007, Extended VIKOR method in comparison with outranking methods, European journal of operational research, 178(2), pp. 514-529.

Pamucar, D., Bozanic, D., Lukovac, V., Komazec, N., 2018, Normalized weighted geometric bonferroni mean operator of interval rough numbers – application in interval rough DEMATEL-COPRAS, Facta Universitatis,-Series Mechanical Engineering, 16(2), pp. 171-191.

Pamučar, D., Božanić, D., 2019, Selection of a location for the development of multimodal logistics center: Application of single-valued neutrosophic MABAC model, Operational research in engineering sciences: Theory and applications, 2(2), pp. 55-71.

Sayadi, M.K., Heydari, M., Shahanaghi, K., 2009, Extension of VIKOR method for decision making problem with interval numbers, Applied Mathematical Modelling, 33(5), pp. 2257-2262.

Jahan, A., 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, pp. 335-342.

Vafaei, N., Ribeiro, R.A., Camarinha-Matos, L.M., 2016, Normalization techniques for multi-criteria decision making: Analytical hierarchy process case study, In Technological innovation for cyber-physical systems, Springer international publishing, pp. 261-269.

Mukhametzyanov, I., Pamucar, D., 2018, A sensitivity analysis in MCDM problems: A statistical approach, Decision making: applications in management and engineering, 1(2), pp. 51-80.

Pamučar, D., Božanić, D., Ranđelović, A., 2017, Multi-criteria decision making: An example of sensitivity analysis, Serbian journal of management, 11(1), pp. 1-27.

Kahraman, Y.R., 2002, Robust sensitivity analysis for multi-attribute deterministic hierarchical value models, Storming Media, Ohio.

Jankovic, A., Popovic, M., 2019, Methods for assigning weights to decision makers in group AHP decision-making, Decision making: applications in management and engineering, 2(1), pp. 147-165.


  • There are currently no refbacks.

ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4