Specific character of objective methods for determining weights of criteria in MCDM problems: Entropy, CRITIC and SD

  • Irik Mukhametzyanov Ufa State Petroleum Technological University, Ufa, Russia
Keywords: 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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References

Ahn, B.S., & Park, K.S. (2008). Comparing methods for multiattribute decision making with ordinal weights. Computers & Operations Research, 35 (5), 1660–1670. DOI: https://doi.org/10.1016/j.cor.2006.09.026

Ali, Z., Mahmood, T., Ullah, K., & Khan, Q. (2021). Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management. Reports in Mechanical Engineering, 2(1), 105-134. DOI: https://doi.org/10.31181/rme2001020105t

Alosta, A., Elmansuri, O., & Badi, I. (2021). Resolving a location selection problem by means of an integrated AHP-RAFSI approach. Reports in Mechanical Engineering, 2(1), 135-142. DOI: https://doi.org/10.31181/rme200102135a

Barron, F.H. (1992). Selecting a best multiattribute alternative with partial information about attribute weights. Acta Psychologica, 80, 91–103. DOI: https://doi.org/10.1016/0001-6918(92)90042-C

Barron, F.H., & Barrett, B.E. (1996). Decision quality using ranked attribute weights. Management Science, 42, 1515–1523. DOI: https://doi.org/10.1287/mnsc.42.11.1515

Barron, H., & Schmidt, C. (1988). Sensitivity analysis of additive multiattribute value models. Operations Research, 36(1), 122-127. DOI: https://doi.org/10.1287/opre.36.1.122

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. DOI: https://doi.org/10.1177/1094428106294734

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. DOI: https://doi.org/10.31181/dmame2003114d

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. DOI: https://doi.org/10.1142/S0219622004001124

Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: The CRITIC method. Computers & Operations Research, 22(7), 763‒770. DOI: https://doi.org/10.1016/0305-0548(94)00059-H

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. DOI: https://doi.org/10.1006/obhd.1997.2694

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. DOI: https://doi.org/10.3390/e18060171

Hwang, C.L., & Yoon K. (1981). Multiple Attributes Decision Making: Methods and Applications. A State-of-the-Art Survey. Berlin: Springer-Verlag , Heidelberg, XI. DOI: https://doi.org/10.1007/978-3-642-48318-9

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: https://doi.org/10.1016/j.matdes.2014.09.022

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. DOI: https://doi.org/10.1007/s00170-011-3366-7

Jarque, C. M., & Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review, 55(2), 163–172. DOI: https://doi.org/10.2307/1403192

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, 399–422. DOI: https://doi.org/10.5267/j.ijiec.2016.1.001

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. DOI: https://doi.org/10.3846/jbem.2010.12

Kirkwood, C.W., & Corner, J.L. (1993). The effectiveness of partial information about attribute weights for ranking alternatives in multiattribute decision making. Organizational Behavior and Human Decision Processes, 54, 456–476. DOI: https://doi.org/10.1006/obhd.1993.1019

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. DOI: https://doi.org/10.1007/s10661-012-2723-9

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. DOI: https://doi.org/10.1016/j.proeng.2011.11.2410

Liang, J., Shi, Z. D., Wierman, M.J. (2016). Information entropy, rough entropy and knowledge granulation in incomplete information systems. International Journal of General Systems, 35, 641–654. DOI: https://doi.org/10.1080/03081070600687668

Lotfi, F. H.; Fallahnejad, R. (2010). Imprecise Shannon’s entropy and multi attribute decision making. Entropy, 12, 53–62. DOI: https://doi.org/10.3390/e12010053

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. DOI: https://doi.org/10.1016/S0377-2217(98)00141-6

Mareschal, B. (1988). Weight stability intervals in multicriteria decision aid. European Journal of Operational Research, 33, 54‒64. DOI: https://doi.org/10.1016/0377-2217(88)90254-8

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.

Milosevic, T., Pamucar, D., Chatterjee, P. (2021). Model for selecting a route for the transport of hazardous materials using a fuzzy logic system. Military Technical Courier, 69(2), 355-390.

Mukhametzyanov, I. & Pamučar, D. (2018). Sensitivity analysis in MCDM problems: A statistical approach. Decision Making: Applications in Management and Engineering, 1(2), 51‒80. DOI: https://doi.org/10.31181/dmame1802050m

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(5), 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.

Pamucar, D., & Savin, L.M. (2020). Multiple-criteria model for optimal off-road vehicle selection for passenger transportation: BWM-COPRAS model. Military Technical Courier, 68(1), 28-64.

Pamucar, D., Ecer, F. (2020). Prioritizing the weights of the evaluation criteria under fuzziness: The fuzzy full consistency method – FUCOM-F. Facta Universitatis, series: Mechanical Engineering. 18(3), pp. 419 - 437.

Pekelman, D., & Sen, S.K. (1974). Mathematical programming models for the determination of attribute weights. Management Science, 20, 1217–1229. DOI: https://doi.org/10.1287/mnsc.20.8.1217

Roberts, R., & Goodwin P. (2002). Weight approximations in multi-attribute decision models. Journal of Multi-Criteria Decision Analysis, 11, 291–303. DOI: https://doi.org/10.1002/mcda.320

Saaty, T. L. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill. DOI: https://doi.org/10.21236/ADA214804

Shirland, L.E., Jesse, R.R., Thompson, R.L., & Iacovou, C.L. (2003). Determining attribute weights using mathematical programming. Omega, 31, 423–437. DOI: https://doi.org/10.1016/S0305-0483(03)00081-1

Singh, A., Ghadai, R.K., Kalita, K., Chatterjee, P., Pamucar, D. (2020). EDM process parameter optimization for efficient machining of Inconel-718. Facta Universitatis, series: Mechanical Engineering. 18(3), pp. 473 - 490.

Solymosi, T., & Dombi, J. (1986). A method for determining the weights of criteria: The centralized weights. European Journal of Operational Research, 26, 35–41. DOI: https://doi.org/10.1016/0377-2217(86)90157-8

Stillwell, W. G., Seaver, D. A., & Edwards, W. (1981). A comparison of weight approximation techniques in multiattribute utility decision making. Organizational Behavior and Human Performance, 28, 62–77. DOI: https://doi.org/10.1016/0030-5073(81)90015-5

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. DOI: https://doi.org/10.1016/0377-2217(87)90249-9

Triantaphyllou, E. (2000). Multi-criteria Decision Making Methods: A Comparative Study (Springer US). DOI: https://doi.org/10.1007/978-1-4757-3157-6

Tzeng, G-H., & Huang, J-J. (2011). Multiple Attribute Decision Making: Methods and Application. Chapman and Hall/CRC. DOI: https://doi.org/10.1201/b11032

Ustinovičius, L. (2001). Determining integrated weights of attributes. Statyba, 7(4), 321–326. DOI: https://doi.org/10.1080/13921525.2001.10531743

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.

Wang, Y.-M., & Luo, Y. (2010). Integration of correlations with standard deviations for determining attribute weights in multiple attribute decision making. Math. Comput. Model., 51, 1–12. DOI: https://doi.org/10.1016/j.mcm.2009.07.016

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. DOI: https://doi.org/10.1016/0377-2217(93)E0343-V

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, 215. DOI: https://doi.org/10.3390/e20040215

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. DOI: https://doi.org/10.1016/j.eswa.2010.10.046

Xu, X. (2004). A note on the subjective and objective integrated approach to determine attribute weights. European Journal of Operational Research, 156, 530–532. DOI: https://doi.org/10.1016/S0377-2217(03)00146-2

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. DOI: https://doi.org/10.3390/e19080396

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. DOI: https://doi.org/10.31181/dmame1902102z

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. DOI: https://doi.org/10.31181/dmame2003149z

Zolfani, S.H.; Yazdani, M.; Pamucar, D. & Zarate, P. (2020). A VIKOR and TOPSIS focused reanalysis of the MADM methods based on logarithmic normalization. Facta universitatis series: Mechanical Engineering, 18(3), 341-355.

Published
2021-06-11
How to Cite
Mukhametzyanov, I. (2021). Specific character of objective methods for determining weights of criteria in MCDM problems: Entropy, CRITIC and SD. Decision Making: Applications in Management and Engineering, 4(2), 76-105. https://doi.org/10.31181/dmame210402076i