Scheme for Statistical Analysis of Some Parametric Normalization Classes

Authors

  • Aleksandras Krylovas Vilnius Gediminas technical University
  • Natalja Kosareva Vilnius Gediminas technical University
  • Edmundas Kazimieras Zavadskas Vilnius Gediminas technical University

Keywords:

normalization methods, multi-criteria optimization, Monte Carlo method, comparative statistical analysis, SAW

Abstract

In this research 7 parametric classes of normalization functions depending on 1 or 2 parameters proposed for MCDM problem solution. Monte Carlo experiments carried out to perform comparative statistical analysis and find optimal parameter values for the case of Gaussian distribution of decision making matrix elements. Optimal parameter values were ascertained for each normalization method. Normalization formulas were compared with each other in the sense of their efficiency. Logarithmic and Max normalization formulas demonstrated highest values of the best alternative identification. The proposed methodology of determining optimal parameter values of normalization formulas could be applied by approximation of real data with appropriate probability distributions.

References

Celen, A. (2014). Comparative Analysis of Normalization Procedures in TOPSIS Method: With an Application to Turkish Deposit Banking Market, Informatica, 25(2), 185-208, 2004.

Chakraborty, S.; Yeh, C.-H. (2009). A Simulation Comparison of Normalization Procedures for TOPSIS, International Conference on Computers and Industrial Engineering (CIE39): Troyes, France, JUL 06-09, 1-3, 1815-1820, 2009. https://doi.org/10.1109/ICCIE.2009.5223811

Hwang, C.L.; Yoon, K. (1981). Multiple attribute decision making - methods and applications, 2nd eds., Springer-Verlag, Berlin, 1981. https://doi.org/10.1007/978-3-642-48318-9

Jahan, A.; Edwards, K.; Kevin, 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, 2005.

Juttler, H. (1966). Untersuchungen zur Fragen der Operationsforschung und ihrer Anwendungs-moglichkeiten auf okonomische Problemstellungen unter besonderer Berucksichtigung der Spieltheorie [Investigations on the question of operational research and its application to economic problems with special consideration of the game theory]: Doctoral dissertation, Fakultat der Humboldt-Universitat, Berlin, 1966.

Kaplinski, O.; TamošaitienË™e, J. (2015). Analysis of Normalization Methods Influencing Results: A Review to Honour Professor Friedel Peldschus on the Occasion of his 75th Birthday, Procedia Engineering, 122, 2-10, 2015. https://doi.org/10.1016/j.proeng.2015.10.001

Kosareva, N.; Krylovas, A.; Zavadskas, E.-K. Statistical analysis of MCDM data normalization methods using Monte Carlo approach. The case of ternary estimates matrix, Economic Computation and Economic Cybernetics Studies and Research. (In Press).

Kou, G.; Ergu, D.; Lin, C.; Chen, Y. (2016). Pairwise comparison matrix in multiple criteria decision making, Technological and Economic Development of Economy, 22(5), 738-765, 2016. https://doi.org/10.3846/20294913.2016.1210694

Li, G.; Kou, G.; Peng, Y. (2018). A Group Decision Making Model for Integrating Heterogeneous Information, IEEE Transactions on Systems, Man, and Cybernetics-System, 48(6), 982-992, 2018. https://doi.org/10.1109/TSMC.2016.2627050

MacCrimmon, K.R. (1968). Decision making among multiple-attribute alternatives: a survey and consolidated approach, No. RM-4823-ARPA, Santa Monica: RAND Corporation, 1968.

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, Struct Multidiscip Optimization, 29(4), 312-318, 2005. https://doi.org/10.1007/s00158-004-0473-1

Peldschus, F. (2018). Recent Findings from Numerical Analysis in Multi-Criteria Decision Making, Technological and Economic Development of Economy, 24(4), 1456-1478, 2018. https://doi.org/10.3846/20294913.2017.1356761

Podviezko, A.; Podvezko, V. (2015). Influence of data transformation on multicriteria evaluation result, Procedia Engineering, 51(1), 151-157, 2015. https://doi.org/10.1016/j.proeng.2015.10.019

Stanujkic, D.; Magdalinovic, N.; Jovanovic, R. (2013). A multi-attribute decision making model based on distance from decision maker's preferences, Informatica, 24(1), 103-118, 2013.

Stanujkic, D.; Zavadskas, E.-K.; Karabasevic, D; Turskis, Z.; KeršulienË™e, V. (2017). New group decision-making ARCAS approach based on the integration of the SWARA and the ARAS methods adapted for negotiations, Journal of Business Economics and Management, 18(4), 599-618, 2017. https://doi.org/10.3846/16111699.2017.1327455

Stopp, F. (1975). Variantenvergleich durch Matrixspiele, Wissenschaftliche Zeitschrift der Hochschule für Bauwesen Leipzig, Heft 2, 1975.

Van Delft, A.; Nijkamp, P. (ed.) (1977). Multi-criteria analysis and regional decision-making, Studies in Applied Regional Science, Springer, 1977.

Weitendorf, D. (1976). Beitrag zur optimierung der räumlichen struktur eines gebäudes: Dissertation A., Weimar: Hochschule für Architektur und Bauwesen, 1976.

Yazdani, M.; Jahan A.; Zavadskas, E.-K. (2017). Analysis in Material Selection: Influence of Normalization Tools on COPRAS-G, Economic Computation and Economic Cybernetics Studies and Research, 51(1), 59-74, 2017.

Zavadskas, E.-K.; Turskis, Z. (2008). A New Logarithmic Normalization Method in Games Theory, Informatica, 19(2), 303-314, 2008.

Published

2018-11-29

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.