How the normalization of the decision matrix influences the results in the VIKOR method?

Abstract Many decisions made in different areas of life require a certain number of criteria to be taken into account to help find the optimal solution. The problem may be to determine whether the way in which we represent the input has an impact on the final result. It means whether or not the normalization affects the results achieved by using multi-criteria decision analysis (MCDA) methods. In this paper, we examine the influence of normalization on the results obtained by the VIKOR method. This issue will be addressed based on the training management problem. First, we prepare the raw decision matrix and its forms after normalizations. According to the VIKOR method, we use a calculating procedure for all cases and compare the obtained rankings using selected similarity coefficients, which showed to what extent these rankings are similar. The results obtained as a result of the conducted research show that the presentation of the input data has an impact on the final obtained rankings.

[1]  Morteza Yazdani,et al.  A state-of the-art survey of TOPSIS applications , 2012, Expert Syst. Appl..

[2]  Ali Jahan,et al.  Material selection for femoral component of total knee replacement using comprehensive VIKOR , 2011 .

[3]  Edmundas Kazimieras Zavadskas,et al.  VIKOR Technique: A Systematic Review of the State of the Art Literature on Methodologies and Applications , 2016 .

[4]  Artur Karczmarczyk,et al.  Generalised framework for multi-criteria method selection , 2018, Omega.

[5]  Muhammet Gulź,et al.  A state of the art literature review of VIKOR and its fuzzy extensions on applications , 2016 .

[6]  D. Radovanović,et al.  Dietary supplements and medications in elite sport – polypharmacy or real need? , 2011, Scandinavian journal of medicine & science in sports.

[7]  S. M. Sapuan,et al.  A comprehensive VIKOR method for material selection , 2011, Materials & Design.

[8]  L. Burke,et al.  Variability in estimation of self-reported dietary intake data from elite athletes resulting from coding by different sports dietitians. , 2003, International journal of sport nutrition and exercise metabolism.

[9]  Eun-Sung Chung,et al.  Fuzzy VIKOR approach for assessing the vulnerability of the water supply to climate change and variability in South Korea , 2013 .

[10]  D. Mould,et al.  Multi-Criteria Decision Analysis Model for Assessing the Risk from Multi-Ingredient Dietary Supplements (MIDS) , 2020, Journal of dietary supplements.

[11]  Jarosław Wątróbski,et al.  Generalised framework for multi-criteria method selection: Rule set database and exemplary decision support system implementation blueprints , 2018, Data in brief.

[12]  María Teresa Lamata,et al.  A comparative analysis of multi-criteria decision-making methods , 2016, Progress in Artificial Intelligence.

[13]  Gwo-Hshiung Tzeng,et al.  A VIKOR technique based on DEMATEL and ANP for information security risk control assessment , 2013, Inf. Sci..

[14]  D. Nemet,et al.  Negative energy balance plays a major role in the IGF-I response to exercise training. , 2004, Journal of applied physiology.

[15]  Serafim Opricovic,et al.  Fuzzy VIKOR with an application to water resources planning , 2011, Expert Syst. Appl..

[16]  Peter L. Kolominsky-Rabas,et al.  Methodological Challenges in Multi-Criteria Decision Analysis (MCDA) for Health Policy Decision-Making: A Systematic Review , 2013 .

[17]  J. Sallis,et al.  Community Interventions to Promote Proper Nutrition and Physical Activity among Youth , 2000 .

[18]  J. Costa,et al.  A WEIGHTED RANK MEASURE OF CORRELATION , 2005 .

[19]  Enrique Mu.  Who really won the FIFA 2014 Golden Ball Award?: What sports can learn from multi-criteria decision analysis , 2016 .

[20]  S. Vinodh,et al.  Application of fuzzy VIKOR and environmental impact analysis for material selection of an automotive component , 2012 .

[21]  C.-L. Chang,et al.  Using the VIKOR method to evaluate the design of a water quality monitoring network in a watershed , 2014, International Journal of Environmental Science and Technology.

[22]  Mohammad Jafar Tarokh,et al.  A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting , 2011, Expert Syst. Appl..

[23]  David Bishop,et al.  Dietary Supplements and Team-Sport Performance , 2010, Sports medicine.

[24]  J. Doyle,et al.  Nutrition for Sport and Exercise , 2007 .

[25]  D. Blest.  Theory & Methods: Rank Correlation — an Alternative Measure , 2000 .

[26]  Nan Liu,et al.  Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment , 2012, Expert Syst. Appl..

[27]  C. Genest,et al.  On blest's measure of rank correlation , 2003 .

[28]  Shahzad Faizi,et al.  Decision Making with Uncertainty Using Hesitant Fuzzy Sets , 2017, International Journal of Fuzzy Systems.

[29]  Gwo-Hshiung Tzeng,et al.  Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS , 2004, Eur. J. Oper. Res..

[30]  Gwo-Hshiung Tzeng,et al.  Extended VIKOR method in comparison with outranking methods , 2007, Eur. J. Oper. Res..