Specific character of objective methods for determining weights of criteria in MCDM problems: Entropy, CRITIC and SD
DOI:
https://doi.org/10.31181/dmame210402076iKeywords:
Multi-criteria decision making, weights estimation, Entropy weighting method, CRITIC method, Standard Deviation method, integrated weighting methods.Abstract
It is carried out a comparative analysis of objective methods for determining the weights of criteria in the problems of multi-criteria decision-making. It is shown that the use of methods for determining the weights of criteria, based on formal processing of the decision matrix (Entropy, CRITIC, Standard deviation) for MCDM problems is not correct. It is demonstrated that the Entropy method is highly sensitive to valuation of probabilities of states based on the decision matrix. For the Entropy method two modifications of estimation of probability of states are proposed that partially eliminate the contradictions of the basic EWM method. The first modification (EWM-DF) is based on a statistical approach and it estimates the probabilities of states based on attribute distribution function. Another modification (EWM-dsp) estimates the probabilities of states based on the relative dispositions of attributes. The options both have supporting rationale. The analysis of integrated weighing methods is carried out and various options for aggregation of weights are given. An integrated EWM-Corr method is proposed which allows to re-allocate the weights obtained by the Entropy method among correlated criteria.
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Ahn, B.S., & Park, K.S. (2008). Comparing methods for multiattribute decision making with ordinal weights. Computers & Operations Research, 35 (5), 1660–1670.
Barron, F.H. (1992). Selecting a best multiattribute alternative with partial information about attribute weights. Acta Psychologica, 80, 91–103.
Barron, F.H., & Barrett, B.E. (1996). Decision quality using ranked attribute weights. Management Science, 42, 1515–1523.
Barron, H., & Schmidt, C. (1988). Sensitivity analysis of additive multiattribute value models. Operations Research, 36(1), 122-127.
Bobko P., Roth, P.L., & Buster, M.A. (2007). The Usefulness of Unit Weights in Creating Composite Scores. A Literature Review, Application to Content Validity, and Meta-Analysis. Organizational Research Methods, 10(4), 689–709.
Chen, P. (2019). Effects of normalization on the entropy-based TOPSIS method. Expert Systems with Applications, 136, 33‒41.
Đalić, I., Stević, Ž., Karamasa, C., & Puška, A. (2020) A Novel Integrated Fuzzy PIPRECIA – Interval Rough Saw Model: Green Supplier Selection. Decision Making: Applications in Management and Engineering, 3(1), 126‒145.
Deng, M., Xu, W., & Yang, J.B. (2004). Estimating the attribute weights through evidential reasoning and mathematical programming. International Journal of Information Technology & Decision Making, 3, 419–428.
Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The CRITIC method. Computers & Operations Research, 22(7), 763‒770.
Doyle, J.R., Green, R.H., & Bottomley, P.A. (1997). Judging relative importance: Direct rating and point allocation are not equivalent. Organizational Behavior and Human Decision Processes, 70, 55–72.
Ginevicius, R., & Podvezko, V. (2005). Objective and subjective approaches to determining the criterion weight in multicriteria models. Proceedings of International Conference RelStat. Transport and Telecommunication, 6(1), 133–137.
Goodwin, P., & Wright, G. (1998). Decision Analysis for Management Judgment. (2nd ed). Chichester: Wiley.
He, D., Xu, J., & Chen, X. (2016). Information-theoretic-entropy based weight aggregation method in multiple-attribute group decision-making. Entropy, 18(6), 171.
Hwang, CL., & Yoon, K. (1981). Methods for Multiple Attribute Decision Making. In: Multiple Attribute Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48318-9_3
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.
Jahan, A., Mustapha, F., Sapuan, S.M., Ismail, M. Y., Bahraminasab, M. (2012). A framework for weighting of criteria in ranking stage of material selection process. The International Journal of Advanced Manufacturing Technology, 58, 411–420.
Jarque, C. M., & Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review, 55(2), 163–172.
Karande, P., Zavadskas, E., & Chakraborty, S. (2016). A study on the ranking performance of some MCDM methods for industrial robot selection problems. International Journal of Industrial Engineering Computations, 7(3), 399-422.
Kersuliene, V., Zavadskas, E. K., & Turskis, Z. (2010). Selection of rational dispute resolution method by applying new step-wise weight assessment ratio analysis (SWARA). Journal of Business Economics and Management, 11(2), 243–258.
Li, P., Qian, H., Wu, J., & Chen, J. (2013). Sensitivity analysis of TOPSIS method in water quality assessment: I. Sensitivity to the parameter weights. Environmental Monitoring and Assessment, 185, 2453–2461.
Li, X., Wang, K,. Liu, L., Xin J., Yang, H., Gao, C. (2011). Application of the Entropy Weight and TOPSIS Method in Safety Evaluation of Coal Mines, Procedia Engineering, First International Symposium on Mine Safety Science and Engineering, 26, 2085-2091.
Liang, J., Shi, Z., Li, D., & Wierman, M. J. (2006). Information entropy, rough entropy and knowledge granulation in incomplete information systems. International Journal of general systems, 35(6), 641-654.
Lotfi, F. H., & Fallahnejad, R. (2010). Imprecise Shannon’s entropy and multi attribute decision making. Entropy, 12(1), 53-62.
Ma, J., Fan, Z. P., & Huang, L. H. (1999). A subjective and objective integrated approach to determine attribute weights. European Journal of Operational Research, 112, 397–404.
Mareschal, B. (1988). Weight stability intervals in multicriteria decision aid. European Journal of Operational Research, 33, 54‒64.
Math Works. File Exchange. Weight of Criteria by Irik Mukhametzyanov (2021). https://www.mathworks.com/matlabcentral/fileexchange/91720-weight-of-criteria Accessed 06 May 2021.
Mukhametzyanov, I., & Pamucar, D. (2018). A sensitivity analysis in MCDM problems: A statistical approach. Decision making: applications in management and engineering, 1(2), 51-80.
Mukhametzyanov, I. Z. (2018). IZ-norm method of normalization the multidimensional data, United States Copyright Office, Reg# TXu002125819/2018-09-28, https://cocatalog.loc.gov/cgi-bin/Pwebrecon.cgi?DB=local&PAGE=First
Mukhametzyanov, I. Z. (2019). A new method for the normalization of multidimensional data (IZ-Method) for MCDM problems, Proc. the 25st International Conference on Multiple Criteria Decision Making (MCDM 2019), Istanbul, Turkey (2019), 96–97.
Mukhametzyanov, I. Z. (2020). ReS-algorithm for converting normalized values of cost criteria into benefit criteria in MCDM tasks. International Journal of Information Technology & Decision Making, 19(05), 1389-1423.
Mukhametzyanov, I. Z. (2021). Elimination of the domains’ displacement of the normalized values in MCDM tasks: the IZ-method. International Journal of Information Technology & Decision Making, [In Press].
Odu, G. O. (2019). Weighting Methods for Multi-Criteria Decision Making Technique. Journal of Applied Sciences and Environmental Management, 23(8), 1449–1457.
Pamučar D., Stević Ž., & Sremac S. (2018). A new model for determining weight coefficients of criteria in MCDM models: Full Consistency Method (FUCOM). Symmetry, 10(9), 393.
Pekelman, D., & Sen, S.K. (1974). Mathematical programming models for the determination of attribute weights. Management Science, 20, 1217–1229.
Roberts, R., & Goodwin P. (2002). Weight approximations in multi-attribute decision models. Journal of Multi-Criteria Decision Analysis, 11, 291–303.
Saaty, T. L. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill.
Shirland, L.E., Jesse, R.R., Thompson, R.L., & Iacovou, C.L. (2003). Determining attribute weights using mathematical programming. Omega, 31, 423–437.
Solymosi, T., & Dombi, J. (1986). A method for determining the weights of criteria: The centralized weights. European Journal of Operational Research, 26, 35–41.
Takeda, E., Cogger, K. O., & Yu, P. L. (1987). Estimating criterion weights using eigenvectors: A comparative study. European Journal of Operational Research, 29, 360–369.
Triantaphyllou, E. (2000). Multi-Criteria Decision Making Methods. In: Multi-criteria Decision Making Methods: A Comparative Study. Applied Optimization, vol 44. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3157-6_2
Tzeng, G. H., & Huang, J. J. (2011). Multiple attribute decision making: methods and applications. CRC press.
Ustinovičius, L. (2001). Determining integrated weights of attributes. Statyba, 7(4), 321–326.
Vinogradova, I., Podvezko, V., & Zavadskas, E.K. (2018). The recalculation of the weights of criteria in MCDM methods using the bayes approach. Symmetry, 10(6), 205.
Von Winterfeldt, D., & Edwards, W. (1986). Decision Analysis and Behavioral Research, Cambridge: Cambridge University Press, MA.
Wolters, W. T. M., & Mareschal, B. (1995). Novel types of sensitivity analysis for additive MCDM methods, European Journal of Operational Research, 81(2), 281‒290.
Wu, D., Wang, N., Yang, Z., Li, C., & Yang, Y. (2018). Comprehensive evaluation of coal-fired power units using grey relational analysis and a hybrid entropy-based weighting method. Entropy, 20(4), 215.
Wu, J., Sun, J., Liang, L., & Zha, Y. (2011). Determination of weights for ultimate cross efficiency using Shannon entropy. Expert Systems with Applications, 38(5), 5162–5165.
Xu, X. (2004). A note on the subjective and objective integrated approach to determine attribute weights. European Journal of Operational Research, 156, 530–532.
Zeleny, M. (1982). Multiple Criteria Decision Making. McGraw-Hill, New York.
Zhao, H., Yao, L., Mei, G., Liu, T., Ning, Y. (2017). A Fuzzy comprehensive evaluation method based on AHP and entropy for landslide susceptibility map. Entropy, 19, 396.
Žižović, M., & Pamucar, D. (2019). New model for determining criteria weights: Level Based Weight Assessment (LBWA) model. Decision Making: Applications in Management and Engineering, 2(2), 126‒137.
Žižović, M., Miljković, B., & Marinković, D. (2020). Objective methods for determining criteria weight coefficients: A modification of the CRITIC method. Decision Making: Applications in Management and Engineering, 3(2), 149-161.
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