Comparative Analysis of the Normalization Techniques in the Context of MCDM Problems

  • Ahmet Aytekin Department of quantitative methods, Artvin Çoruh University, Turkey
Keywords: Data, Scaling, MCDM, Normalization

Abstract

NormNormalization is an essential step in data analysis and for MCDM methods. This study aims to outline the positive and negative features of the normalization techniques that can be used in MCDM problems. In order to compare the different normalization techniques, fourteen sets representing different scenarios of decision problems were used. According to the results, if the decision-maker chooses to take the alternative with the highest value in the criteria and avoid the one with the lowest value, or vice versa, optimization-based normalization techniques should be preferred, whereas the reference-based normalization techniques are considered appropriate for situations where there are ideal values determined by the decision-maker for each criterion. However, if the decision-maker believes that the values in the criteria do not represent the monotonous increasing or decreasing benefit/cost, then non-linear normalization techniques should be used. Also, in the event of a change in the conditions mentioned above, the decision maker may opt for mixed normalization techniques. However, some data structures, such as the presence of zero, and negative values in the decision matrix, can prevent the use of some normalization techniques. The choice of the normalization technique may also be affected by the problem of rank reversal, the range of normalized values, obtaining the same optimization aspect for all criteria, and the validity of results.

Downloads

Download data is not yet available.

References

Alpar, R. (2013). Uygulamalı çok değişkenli istatistik yöntemler. Detay Yayıncılık, Ankara.

Aytekin, A. (2020). Çok kriterli karar problemine uzaklık ve referans temelli çözüm yaklaşımı [Unpublished PhD thesis]. Anadolu University, Eskişehir.

Brauers, W. K., & Zavadskas, E. K. (2006). The MOORA method and its application to privatization in a transition economy. Control and Cybernetics, 35, 445-469.

Chakraborty, S., & 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. Conf. on Artificial Intelligence, Knowledge Engineering and Data Bases, 6, 102-109.

Chakraborty, S., & Yeh, C. H. (2009). A simulation comparison of normalization procedures for TOPSIS. In 2009 International Conference on Computers & Industrial Engineering (pp. 1815-1820). IEEE.

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.

Çelen, A. (2014). Comparative analysis of normalization procedures in TOPSIS method: With an application to Turkish deposit banking market. Informatica, 25(2), 185-208.

Durucasu, H., Aytekin, A., Saraç, B., & Orakçı, E (2017). Current application fields of ELECTRE and PROMETHEE: A literature review. Alphanumeric Journal, 5(2), 229-270. doi.org/10.17093/alphanumeric.320235

e Costa, C. A. B., & Vansnick J. C. (1994). MACBETH—An interactive path towards the construction of cardinal value functions. International Transactions in Operational Research, 1(4), 489-500.

Gardziejczyk, W., & Zabicki, P. (2017). Normalization and variant assessment methods in selection of road alignment variants–case study. Journal of Civil Engineering and Management, 23(4), 510-523. doi.org/10.3846/13923730.2016.1210223

Fayazbakhsh, K., Abedian, A., Manshadi, B. D., & Khabbaz R.S. (2009). Introducing a novel method for materials selection in mechanical design using Z-transformation in statistics for normalization of material properties. Materials & Design, 30(10), 4396-404. doi.org/10.1016/j.matdes.2009.04.004

Jahan, A., Mustapha, F., Ismail, M. Y., Sapuan, S. M., & Bahraminasab, M. (2011). A comprehensive VIKOR method for material selection. Materials & Design, 32(3), 1215-1221. doi.org/10.1016/j.matdes.2010.10.015

Jahan, A., Bahraminasab, M., & Edwards, K. L. (2012). A target-based normalization technique for materials selection. Materials & Design, 35: 647-654. doi.org/10.1016/j.matdes.2011.09.005

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, 335-342. doi.org/10.1016/j.matdes.2014.09.022

Jensen, R. E. (1984). An alternative scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 28(3), 317-332.

Kainulainen, T., Leskinen, P., Korhonen, P., Haara, A., & Hujala, T. (2009). A statistical approach to assessing interval scale preferences in discrete choice problems. Journal of the Operational Research Society, 60(2), 252-258.

Lootsma, F.A. (1999). Multi-criteria decision analysis via ratio and difference judgement (Vol. 29), Kluwer Academic Publishers, Dordrecht.

Milani, A.S., Shanian, A., Madoliat, R., & 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.

Özdağoğlu, A. (2013). Çok ölçütlü karar verme modellerinde normalizasyon tekniklerinin sonuçlara etkisi: COPRAS örneği. Eskişehir Osmangazi Üniversitesi İktisadi ve İdari Bilimler Dergisi, 8(2), 229-255.

Özdağoğlu, A. (2014). Normalizasyon yöntemlerinin çok ölçütlü karar verme sürecine etkisi–MOORA yöntemi incelemesi. Ege Academic Review, 14(2), 283-294.

Pavličić, D. (2001). Normalization affects the results of MADM methods. Yugoslav Journal Of Operations Research, 11(2), 251-265.

Podviezko, A., & Podvezko V (2015). Influence of data transformation on multi-criteria evaluation result. Procedia Engineering, 122, 151-157. doi.org/10.1016/j.proeng.2015.10.019

Roberts, F. S. (1984). Measurement theory: With applications to decisionmaking, utility, and the social sciences (Encyclopedia of mathematics and its applications). Cambridge University Press. doi.org/10.1017/CBO9780511759871

Roy, J., Sharma, H. K., Kar, S., Zavadskas, E. K., & Saparauskas, J. (2019). An extended COPRAS model for multi-criteria decision-making problems and its application in web-based hotel evaluation and selection. Economic research-Ekonomska istraživanja, 32(1), 219-253. doi.org/10.1080/1331677X.2018.1543054

Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281.

Saranya, C., & Manikandan, G. (2013). A study on normalization techniques for privacy preserving data mining. International Journal of Engineering and Technology (IJET), 5(3), 2701-2704.

Sarraf, A.Z., Mohaghar, A., & Bazargani H. (2013). Developing TOPSIS method using statistical normalization for selecting knowledge management strategies. Journal of Industrial Engineering and Management, 6(4), 860-875. doi.org/10.3926/jiem.573

Sharma, H. K., Roy, J., Kar, S., & Prentkovskis, O. (2018). Multi criteria evaluation framework for prioritizing indian railway stations using modified rough AHP-MABAC method. Transport and telecommunication journal, 19(2), 113-127. doi.org/10.2478/ttj-2018-0010

Shih, H. S., Shyur H. J., & Lee E. S. (2007). An extension of TOPSIS for group decision making. Mathematical and Computer Modelling, 45(8), 801-13. doi.org/10.1016/j.mcm.2006.03.023

Tavşancıl, E. (2006). Tutumların ölçülmesi ve SPSS ile veri analizi. Ankara, Nobel.

Vafaei, N., Ribeiro, R. A., & 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. Springer, Cham, 261-269.

Vafaei, N., Ribeiro, R.A., & Camarinha-Matos, L.M. (2018a). Data normalisation techniques in decision making: case study with TOPSIS method. International Journal of Information and Decision Sciences, 10(1), 19-38. doi.org/10.1504/IJIDS.2018.090667

Vafaei, N., Ribeiro, R. A., & Camarinha-Matos, L. M. (2018b). Selection of normalization technique for weighted average multi-criteria decision making. In Doctoral Conference on Computing, Electrical and Industrial Systems. Springer, Cham, 43-52.

Wu, H. H. (2002). A comparative study of using grey relational analysis in multiple attribute decision making problems. Quality Engineering, 15(2), 209-17.

Wu, W. (2008). Choosing knowledge management strategies by using a combined ANP and DEMATEL approach. Expert Systems with Applications, 35(3), 828-835.

Yoon, K., & Kim, G. (1989). Multiple attribute decision analysis with imprecise information. IIE Transactions. 21(1), 21-26.

Zavadskas, E.K, & Turskis Z. (2008). A new logarithmic normalization method in games theory. Informatica. 19(2), 303-14.

Zeng Q. L., Li D. D., & Yang Y. B. (2013). VIKOR method with enhanced accuracy for multiple criteria decision making in healthcare management. Journal of Medical Systems. 37(2), 9908.

Zhou, P., Ang B. W., & Poh K. L. (2006). Comparing aggregating methods for constructing the composite environmental index: An objective measure. Ecological Economics, 59(3), 305-311.

Published
2021-03-21
How to Cite
Aytekin, A. (2021). Comparative Analysis of the Normalization Techniques in the Context of MCDM Problems. Decision Making: Applications in Management and Engineering, 4(2), 1-25. https://doi.org/10.31181/dmame210402001a