Determining the appropriate weights of criteria in multi-criteria decision-making using cooperative game: A case study of bank
الموضوعات :Seyed Hadi Mousavi-Nasab 1 , Jalal Safari 2 , Ashkan Hafezalkotob 3
1 - Department of Industrial Engineering, Science and Research Branch ,Islamic Azad University, Tehran, Iran
2 - Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran
3 - College of Industrial engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
الکلمات المفتاحية: TOPSIS, Data encelopment analysis, Shannon Entropy, Shapley value,
ملخص المقالة :
Criteria weighting is a crucial step in the entire decision-making process. Determining the appropriate weights will lead to more reliable results. This study aims to use a coalitional game method for calculating proper criteria weights in multi-criteria decision-making (MCDM). In this paper, the Shapley value method is used to determine the weight of criteria. A numerical case study of 65 banks has been used to explain the efficiency of the proposed method. To this end, using the TOPSIS technique, the alternatives are ranked once in Shapley value and again in the Shannon entropy weighted matrix. Then the results are obtained applying Spearman rank correlation coefficient are compared to efficiency-based ranking using data envelopment analysis (DEA) as a powerful benchmarking method. In the proposed method, unlike many conventional weighting methods, the selection of criteria weights is made in a coalitional game with the participation of all criteria; the obtained weights are both intuitively and objectively fairer, and more reliable rankings are provided. According to the logical and fair calculation of weights, having a simple and understandable mathematical method, and no need for experts’ judgment, the proposed method can be used in real problems. Especially where realistic ranking has a significant impact on the equitable allocation and absorption of resources.
[1] Avkiran, N.K., and Morita, H., Predicting Japanese bank stock performance with a composite relative efficiency metric: A new investment tool, Pacific-Basin Finance Journal, 2010, 18 (3), P.254-271. Doi: 10.1016/j.pacfin.2010.01.002
[2] Baldwin, K., Alhalboni, M., and Helmi, M.H., A structural model of “alpha” for the capital adequacy ratios of Islamic banks, Journal of International Financial Markets, Institutions and Money, 2019, 60, P.267-283. Doi: 10.1016/j.intfin.2018.12.015
[3] Biondi, Y., and Graeff, I., Rethinking bank shareholder equity: The case of Deutsche Bank, In Accounting Forum, 2017, 41 (4), P. 318-335. Doi: 10.1016/j.accfor.2017.06.003
[4] Casajus, A., and Huettner, F., Null, nullifying, or dummifying players: The difference between the Shapley value, the equal division value, and the equal surplus division value, Economics Letters, 2014, 122 (2), P. 167-169. Doi: 10.1016/j.econlet.2013.11.008
[5] Charnes, A., Cooper, W.W., and Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 1987, 2 (6), P. 429–444. Doi: 10.1016/0377-2217(78)90138-8
[6] Chou, C-C., Application of ANP to the selection of shipping registry: The case of Taiwanese maritime industry, International Journal of Industrial Ergonomics, 2018, 67, P. 89-97. Doi: 10.1016/j.ergon.2018.04.009
[7] Diakoulaki, D., Mavrotas, G., and Papayannakis, L., Determining objective weights in multiple indexes problems: the CRITIC method, Computers & Operations Research, 1995, 22 (7), P. 763-770. Doi: 10.1016/0305-0548(94)00059-H
[8] Farrell, M.J., The Measurement of Productive Efficiency, Journal of the Royal Statistical Society, 1957, 120 (3), P. 253- 281. Doi: 10.2307/2343100
[9] Feizabadi, J., and Alibakhshi, S., Synergistic effect of cooperation and coordination to enhance the firm's supply chain adaptability and performance, Benchmarking: An International Journal, 2022, 29 (1), P. 136-171. Doi: 10.1108/BIJ-11-2020-0589
[10] He, Y., Yang, J., and Chen, X., Allocating river water in a cooperative way: a case study of the Dongjiang River Basin, South China, Stochastic Environmental Research and Risk Assessment, 2018, 32 (11), P. 3083-3097. Doi: 10.1007/s00477-018-1526-0
[11] Hwang, C., and Yoon, K., Multiple Attribute Decision Making: Methods and Applications A State-of-the-Art Survey, Springer Berlin Heidelberg, 1981. Doi: 10.1007/978-3-642-48318-9
[12] Izadikhah, M. Financial Assessment of Banks and Financial Institutes in Stock Exchange by Means of an Enhanced Two stage DEA Model. Advances in Mathematical Finance and Applications, 2021, 6(2), P. 207-232. Doi: 10.22034/amfa.2020.1910507.1491
[13] Jahangoshai Rezaee, M., Using Shapley value in multi-objective data envelopment analysis: Power plants evaluation with multiple frontiers, International Journal of Electrical Power & Energy Systems, 2015, 69, P. 141-149. Doi: 10.1016/j.ijepes.2015.01.012
[14] Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., Jafari, Y., and Maddahi, R., Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation, Applied Mathematical Modelling, 2011, 35 (1), P. 544-549. Doi: 10.1016/j.apm.2010.07.020
[15] Jing, YY., Bai, H., and Wang, JJ., A fuzzy multi-criteria decision-making model for CCHP systems driven by different energy sources, Energy Policy, 2012, 42, P. 286– 296. Doi: 10.1016/j.enpol.2011.11.085
[16] Kaviani, M.A., Peykam, A., Khan, S.A., Brahimi, N. and Niknam, R., A new weighted fuzzy programming model for supplier selection and order allocation in the food industry, Journal of Modelling in Management, 2020, 15 (2), P. 381-406. Doi: 10.1108/JM2-11-2018-0191
[17] Kilic, H.S., Demirci, A.E., and Delen, D., An integrated decision analysis methodology based on IF-DEMATEL and IF-ELECTRE for personnel selection, Decision Support Systems, 2020, 137, P. 113360. Doi: 10.1016/j.dss.2020.113360
[18] Liang, P., Hu, J., Liu, Y., and Chen, X., Public resources allocation using an uncertain cooperative game among vulnerable groups", Kybernetes, 2018, 48 (8), P. 1606-1625. Doi: 10.1108/K-03-2018-0146
[19] Lozano, S., Information sharing in DEA: A cooperative game theory approach, European Journal of Operational Research, 2012, 222 (3), P. 558-565. Doi: 10.1016/j.ejor.2012.05.014
[20] Lv, L., Deng, Z., Meng, H., Liu, T., and Wan, L., A multi-objective decision-making method for machining process plan and an application, Journal of Cleaner Production, 2020,260, P.12107. Doi: 10.1016/j.jclepro.2020.121072
[21] Memarpour, M., Hafezalkotob, A., Khalilzadeh, M., Saghaei, A., and Soltani, R., Determining the interest rate on deposits in the Iranian banking system: cooperative or competitive game between the central bank and followers?, Advances in Mathematical Finance and Applications, 2021, Doi: 10.22034/amfa.2021.1931633.1598
[22] Moslemi, A., Pourzamani, Z., and Jahanshad, A. Ranking of Banks’ Risk Reporting Using Data Envelopment Analysis. Advances in Mathematical Finance and Applications, 2021, 6(4), P. 695-715. Doi: 10.22034/amfa.2021.1899631.1436
[23] Mousavi-Nasab, S.H., Safari, J., and Hafezalkotob, A., Resource allocation based on overall equipment effectiveness using cooperative game, Kybernetes, 2019, 49 (3), P. 819-834. Doi: 10.1108/K-09-2018-0491
[24] Mousavi-Nasab, S.H., and Sotoudeh-Anvari, A., A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems, Materials and Design, 2017, 121, P. 237-253. Doi: 10.1016/j.matdes.2017.02.041
[25] Poordavoodi, A., Reza, M., Haj, H., Rahmani, A. M., Izadikhah, M., Toward a More Accurate Web Service Selection Using Modified Interval DEA Models with Undesirable Outputs. CMES-Computer Modeling in Engineering & Sciences, 2020, 123(2), P. 525–570. Doi: 10.32604/cmes.2020.08854
[26] Azadi, M., Izadikhah, M., Ramezani, F., Hussain, F.K., A mixed ideal and anti-ideal DEA model: an application to evaluate cloud service providers, IMA Journal of Management Mathematics, 2000, 31(20), P. 233–256, Doi: 10.1093/imaman/dpz012
[27] Mousavi-Nasab, S.H., and Sotoudeh-Anvari, A., An extension of best-worst method with D numbers: Application in evaluation of renewable energy resources, Sustainable Energy Technologies and Assessments, 2020, 40, P. 100771. Doi: 10.1016/j.seta.2020.100771
[28] Omrani, H., Gharizadeh Beiragh, R., and Shafiei Kaleibari, S., Performance assessment of Iranian electricity distribution companies by an integrated cooperative game data envelopment analysis principal component analysis approach, Electrical Power and Energy Systems, 2015, 64, P. 617–625. Doi: 10.1016/j.ijepes.2014.07.045
[29] Pamučar, D., Stević, Ž., and Sremac, S., A New Model for Determining Weight Coefficients of Criteria in MCDM Models: Full Consistency Method (FUCOM) , Symmetry, 2018, 10 (9), P. 393. Doi: 10.3390/sym10090393
[30] Raju, K., and Kumar, D., Multicriterion decision making in irrigation planning, Agricultural Systems, 1999, 62 (2), P. 117–129. Doi: 10.1016/S0308-521X(99)00060-8
[31] Razmi, J., Hassani, A., and Hafezalkotob, A., Cost saving allocation of horizontal cooperation in restructured natural gas distribution network, Kybernetes, 2018, 47 (6), P. 1217- 1241. Doi: 10.1108/K-04-2017-0126
[32] Rezaei, J., Best-worst multi-criteria decision-making method, Omega, 2015, 53, P. 49–57. Doi: 10.1016/j.omega.2014.11.009
[33] Roberts, R., and Goodwin, P., Weight approximations in multi-attribute decision models, Journal of Multi-Criteria Decision Analysis, 2002, 11 (6), P. 291-303. Doi: 10.1002/mcda.320
[34] Sadeghi A., Larimian T., and Molabashi A., Evaluation of renewable energy sources for generating electricity in province of Yazd: a fuzzy MCDM approach, Procedia-Social and Behavioral Sciences, 2012, 62, P.1095–1099. Doi: 10.1016/j.sbspro.2012.09.187
[35] San Cristobal JR., Multi-criteria decision-making in the selection of a renewable energy project in Spain: the Vikor method, Renewable Energy, 2011, 36, P. 498–502. Doi: 10.1016/j.renene.2010.07.031
[36] Şengul, U., Eren, M., Shiraz, SE., Gezder, V., and Şengul, AB., Fuzzy TOPSIS method for ranking renewable energy supply systems in Turkey, Renew Energy ,2015, 75, P. 617–625. Doi: 10.1016/j.renene.2014.10.045
[37] Shannon, CE., The mathematical theory of communication, A Mathematical Theory of Communication, 1947, 27 (3), P. 379-423. Doi: 10.1002/j.1538-7305.1948.tb01338.x
[38] Shapley, L.S., A Value for n-Person Games, Annals of Mathematics Studies, 1953, 28, P. 307-317. Doi: 10.1515/9781400881970-018
[39] Shih, H-S., Shyur, H-J., and Lee, E.S., An extension of TOPSIS for group decision making, Mathematical and Computer Modelling, 2007,45, (7–8), P. 801-813. Doi: 10.1016/j.mcm.2006.03.023
[40] Yadegari, D., and Avakh Darestani, S., Supplier evaluation with order allocation in mega-projects, Management Research Review, 2021, 44 (8), P. 1157-1181. Doi: 10.1108/MRR-04-2020-0220
[41] Yang, X., and Morita, H., Efficiency improvement from multiple perspectives: An application to Japanese banking industry, Omega, 2013, 41 (3), P. 501-509. Doi: 10.1016/j.omega.2012.06.007
[42] Yang, Z., and Zhang, Q., Resource allocation based on DEA and modified Shapley value, Applied Mathematics and Computation, 2015, 263, P. 280-286. Doi: 10.1016/j.amc.2015.04.063
[43] Yazdani-Chamzini A., and Fouladgar MM., Selecting the optimal renewable energy using multi criteria decision making, Journal of Business Economics and Management, 2013, 14, P.957–978. Doi: 10.3846/16111699.2013.766257
[44] Zolfani, SH., Yazdani, M., and Zavadskas, EK., An extended stepwise weight assessment ratio analysis (SWARA) method for improving criteria prioritization process. Soft Computing, 2018, 22 (22), P. 7399–7405. Doi: 10.1007/s00500-018-3092-2
[45] Zamani, S., Zanjirdar, M., Lalbar, A. The effect of information disclosure on market reaction with meta-analysis approach. Advances in Mathematical Finance and Applications, 2022, 7(3), P. 629-644. Doi: 10.22034/amfa.2021.1937478.1625
[46] Zanjirdar, M., Overview of Portfolio Optimization Models. Advances in Mathematical Finance and Applications, 2020. 5(4), P.419-435. Doi: 10.22034/amfa.2020.674941.
[47] Zanjirdar, M., Kasbi, P., Madahi, Z., Investigating the effect of adjusted DuPont ratio and its components
on investor & quot; s decisions in short and long term, Management Science Letters, 2014, 4(3), P.591-596.
Doi: 10.5267/j.msl.2014.1.003
