How strongly do rank similarity coefficients differ used in decision making problems?

Abstract It is common practice in the MCDA to use several multi-criteria decision methods and then compares obtained rankings with one or two different rank correlation coefficients. The problem is that different rank correlation coefficient gives different values for the same pair of rankings, and the number of studies which tries to investigate it is small. Studying the similarity of rankings is a very important challenge in multi-criteria decision support, and the coefficients themselves seem to be the most practical ways of evaluating rankings. This paper compares chosen rank correlation coefficients to show how much different they are. Spearman’s, Weighted Spearman’s, Kendall Tau and Rank similarity correlation coefficient are compared statistically. The paper confirms that the coefficients are closely related, and their dependence is graphically represented, which initiates research towards allows for their better selection in the future. In conclusions, directions of further development are indicated.

[1]  Wojciech Sałabun,et al.  Efficiency of Methods for Determining the Relevance of Criteria in Sustainable Transport Problems: A Comparative Case Study , 2020, Sustainability.

[2]  H. Di̇nçer,et al.  A multidimensional outlook to energy investments for the countries with continental shelf in East Mediterranean Region with Hybrid Decision Making Model based on IVIF logic , 2021 .

[3]  María Carmen Carnero,et al.  Waste Segregation FMEA Model Integrating Intuitionistic Fuzzy Set and the PAPRIKA Method , 2020 .

[4]  L. Myers,et al.  Spearman Correlation Coefficients, Differences between , 2004 .

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

[6]  L. A. Goodman,et al.  Measures of association for cross classifications , 1979 .

[7]  P. Dickinson,et al.  Extensions of a monte-carlo comparison of some properties of two rank correlation coefficients in small samples , 1974 .

[8]  J. Behnamian,et al.  Strategic supplier selection based on modified sandcone theory and alignment principle , 2021 .

[9]  Bartlomiej Kizielewicz,et al.  Handling economic perspective in multicriteria model - renewable energy resources case study , 2020, KES.

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

[11]  E. S. Pearson,et al.  TESTS FOR RANK CORRELATION COEFFICIENTS. I , 1957 .

[12]  Wojciech Sałabun,et al.  A New Coefficient of Rankings Similarity in Decision-Making Problems , 2020, ICCS.

[13]  Bartłomiej Kizielewicz,et al.  Identification of Relevant Criteria Set in the MCDA Process—Wind Farm Location Case Study , 2020, Energies.

[14]  Jarosław Wątróbski,et al.  Guideline for MCDA Method Selection in Production Management Area , 2016 .

[15]  Zoltán Kaló,et al.  Multiple Criteria Decision Analysis for Health Care Decision Making--Emerging Good Practices: Report 2 of the ISPOR MCDA Emerging Good Practices Task Force. , 2016, Value in health : the journal of the International Society for Pharmacoeconomics and Outcomes Research.

[16]  Mohammad Ebrahim Banihabib,et al.  Comparison of Different Multi Criteria Decision-Making Models in Prioritizing Flood Management Alternatives , 2015, Water Resources Management.

[17]  Fernando Ferreira,et al.  Evaluating retail banking service quality and convenience with MCDA techniques: a case study at the bank branch level , 2014 .

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

[19]  B. Roy,et al.  The European school of MCDA: Emergence, basic features and current works , 1996 .

[20]  H. Abdi The Kendall Rank Correlation Coefficient , 2007 .

[21]  Wojciech Salabun,et al.  Are MCDA Methods Benchmarkable? A Comparative Study of TOPSIS, VIKOR, COPRAS, and PROMETHEE II Methods , 2020, Symmetry.

[22]  Guiwu Wei,et al.  Pythagorean fuzzy heronian mean operators in multiple attribute decision making and their application to supplier selection , 2019, Int. J. Knowl. Based Intell. Eng. Syst..

[23]  Alessandra Oppio,et al.  Combining spatial analysis with MCDA for the siting of healthcare facilities , 2018, Land Use Policy.

[24]  Wojciech Salabun,et al.  A New Approach to Eliminate Rank Reversal in the MCDA Problems , 2021, ICCS.

[25]  Shahzad Faizi,et al.  Best-Worst method and Hamacher aggregation operations for intuitionistic 2-tuple linguistic sets , 2021, Expert Syst. Appl..

[26]  Wojciech Salabun,et al.  Fuzzy Model Identification Using Monolithic and Structured Approaches in Decision Problems with Partially Incomplete Data , 2020, Symmetry.

[27]  Xinchang Zhang,et al.  Regional Land Eco-Security Evaluation for the Mining City of Daye in China Using the GIS-Based Grey TOPSIS Method , 2021 .

[28]  M. Mukaka,et al.  Statistics corner: A guide to appropriate use of correlation coefficient in medical research. , 2012, Malawi medical journal : the journal of Medical Association of Malawi.

[29]  B. W. Ang,et al.  Comparing MCDA Aggregation Methods in Constructing Composite Indicators Using the Shannon-Spearman Measure , 2009 .