Abstract
Generalized grey target decision method (GGTDM) for mixed attributes has different decision-making bases (DMBs) owing to different mechanisms. A combination GGTDM based on zero-sum game theory is proposed to obtain the desirable decision-making effect by fully using the characteristics and information of different DMB based GGTDMs. First, two players are set to compete in the zero-sum game. One player takes different DMB based GGTDMs as the set of his strategies, while the other player adopts the alternatives as the other player’s set of strategies. Then, the ranking values of all alternatives decided by different GGTDMs are converted into scores by equivalent way, and the scores are regarded as the payoffs of the two players. Next, the zero-sum game based linear programming model is built to obtain the solutions when reaching the Nash equilibrium. Finally, the combination decision-making values of all alternatives can be calculated based on the strategy solutions for all GGTDMs. And the decision making is based on the value with which the smaller the better. The application analysis verifies that the proposed method has its feasible and can make full use of the advantages of different DMB based GGTDMs and avoid their shortcomings.
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Abdel-Basset M, Gamal A, Chakrabortty RK, Ryan M (2021) A new hybrid multi-criteria decision-making approach for location selection of sustainable offshore wind energy stations: a case study. J Clean Prod 280:124462. https://doi.org/10.1016/j.jclepro.2020.124462
Animah I (2019) A fuzzy analytical hierarchy process–weighted linear combination decision-making model for prioritization of ballast water treatment technologies by ship owners in Ghana. Proc Inst Mech Eng 233
Büyüközkan G, Çifçi G (2012) A novel hybrid MCDM approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy TOPSIS to evaluate green suppliers. Expert Syst Appl 39:3000–3011. https://doi.org/10.1016/j.eswa.2011.08.162
Büyüközkan G, Güleryüz S (2016) An integrated DEMATEL-ANP approach for renewable energy resources selection in Turkey. Int J Prod Econ 182:435–448. https://doi.org/10.1016/j.ijpe.2016.09.015
Deng J (2002) Grey System Theory Vol. Huangzhong University of Science and Technology Press, Wuhan
Deng X, Jiang W (2019) D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment. Int J Approx Reason 106:194–213. https://doi.org/10.1016/j.ijar.2019.01.007
Ding Z, Jiang Z, Zhang H, Cai W, Liu Y (2020) An integrated decision-making method for selecting machine tool guideways considering remanufacturability. Int J Comput Integ M 33:686–700. https://doi.org/10.1080/0951192X.2018.1550680
Gigović L, Pamučar D, Božanić D, Ljubojević S (2017) Application of the GIS-DANP-MABAC multi-criteria model for selecting the location of wind farms: a case study of Vojvodina. Serbia Renew Energ 103:501–521. https://doi.org/10.1016/j.renene.2016.11.057
Hafezalkotob A, Hafezalkotob A (2017) A novel approach for combination of individual and group decisions based on fuzzy best-worst method. Appl Soft Comput 59:316–325. https://doi.org/10.1016/j.asoc.2017.05.036
Heidary Dahooie J, Razavi Hajiagha SH, Farazmehr S, Zavadskas EK, Antucheviciene J (2021) A novel dynamic credit risk evaluation method using data envelopment analysis with common weights and combination of multi-attribute decision-making methods. Comput Oper Res 129:105223. https://doi.org/10.1016/j.cor.2021.105223
Kumar K, Garg H (2018a) Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Appl Intell 48:2112–2119. https://doi.org/10.1007/s10489-017-1067-0
Kumar K, Garg H (2018b) TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37:1319–1329. https://doi.org/10.1007/s40314-016-0402-0
Lai C, Chen X, Chen X, Wang Z, Wu X, Zhao S (2015) A fuzzy comprehensive evaluation model for flood risk based on the combination weight of game theory. Nat Hazards 77:1243–1259. https://doi.org/10.1007/s11069-015-1645-6
Liao H, Wu X, Mi X, Herrera F (2020) An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule. Omega (Oxford) 93:102052. https://doi.org/10.1016/j.omega.2019.03
Liu T, Deng Y, Chan F (2018) Evidential supplier selection based on DEMATEL and game theory. Int J Fuzzy Syst 20:1321–1333. https://doi.org/10.1007/s40815-017-0400-4
Ma J (2018a) Generalised grey target decision method for mixed attributes with index weights containing uncertain numbers. J Intell Fuzzy Syst 34:625–632. https://doi.org/10.3233/JIFS-17851
Ma J (2018b) Generalized grey target decision method for mixed attributes based on Kullback–Leibler distance. Entropy Switz 20:523. https://doi.org/10.3390/e20070523
Ma J (2019a) Gini-Simpson index based generalised grey target decision method for mixed attributes. J Intell Fuzzy Syst 37:2597–2608. https://doi.org/10.3233/JIFS-182821
Ma J (2019b) Generalised grey target decision method for mixed attributes based on the improved Gini-Simpson index. Soft Comput 23:13449–13458. https://doi.org/10.1007/s00500-019-03883-x
Ma J (2019c) Generalised grey target decision method based on the Gini-Simpson index involving mixed attributes and uncertain numbers. Data Technol Appl 53:484–500. https://doi.org/10.1108/DTA-02-2019-0019
Ma J (2019d) Generalised grey target decision method with index and weight both containing mixed attribute values based on improved Gini-Simpson index. In: statistics & information forum 34:28-34
Ma J, Ji C (2014) Generalized grey target decision method for mixed attributes based on connection number. J Appl Math 2014:8. https://doi.org/10.1155/2014/763543
Ma J, Ma X, Yue J, Tian D (2020) Kullback–Leibler distance based generalized grey target decision method with index and weight both containing mixed attribute values. IEEE Access 8:162847–162854. https://doi.org/10.1109/ACCESS.2020.3020045
Ma J, Tian D, Yue J (2021) A novel generalized grey target decision method with index and weight both containing mixed types of data. Grey Syst Theory Appl 12:252–268. https://doi.org/10.1108/GS-09-2020-0125
Marttunen M, Lienert J, Belton V (2017) Structuring problems for multi-criteria decision analysis in practice: a literature review of method combinations. Eur J Oper Res 263:1–17. https://doi.org/10.1016/j.ejor.2017.04.041
Moslem S, Gul M, Farooq D, Celik E, Ghorbanzadeh O, Blaschke T (2020) An integrated approach of best-worst method (BWM) and triangular fuzzy sets for evaluating driver behavior factors related to road safety. Mathematics (Basel) 8:414. https://doi.org/10.3390/math8030414
Mousavi-Nasab SH, Sotoudeh-Anvari A (2017) A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems. Mater Design 121:237–253. https://doi.org/10.1016/j.matdes.2017.02.041
Nusrat E, Yamada K (2013) A descriptive decision-making model under uncertainty: combination of Dempster-Shafer theory and prospect theory. Int J uncertain Fuzziness Knowl Based Syst 21:79–102. https://doi.org/10.1142/S0218488513500050
Peker M (2016) A decision support system to improve medical diagnosis using a combination of k-medoids clustering based attribute weighting and SVM. J Med Syst. https://doi.org/10.1007/s10916-016-0477-6
Sánchez-Lozano JM, Serna J, Dolón-Payán A (2015) Evaluating military training aircrafts through the combination of multi-criteria decision making processes with fuzzy logic. a case study in the Spanish air force academy. Aerosp Sci Technol 42:58–65. https://doi.org/10.1016/j.ast.2014.12.028
Sun L, Liu Y, Zhang B, Shang Y, Yuan H, Ma Z (2016) An integrated decision-making model for transformer condition assessment using game theory and modified evidence combination extended by D numbers. Energies 9:697. https://doi.org/10.3390/en9090697
Tian Z, Wang J, Zhang H (2018) An integrated approach for failure mode and effects analysis based on fuzzy best-worst, relative entropy, and VIKOR methods. Appl Soft Comput 72:636–646. https://doi.org/10.1016/j.asoc.2018.03.037
Wang J, Pang W, Wang L, Pang X, Yokoyama R (2017) Synthetic evaluation of steady-state power quality based on combination weighting and principal component projection method. CSEE J Power Energy Syst 3:160–166. https://doi.org/10.17775/CSEEJPES.2017.0020
Wu X, Liao H, Xu Z, Hafezalkotob A, Herrera F (2018) Probabilistic linguistic MULTIMOORA: a multicriteria decision making method based on the probabilistic linguistic expectation function and the improved borda rule. IEEE Trans Fuzzy Syst 26:3688–3702. https://doi.org/10.1109/TFUZZ.2018.2843330
Yang M, Zhu H, Guo K (2020) Research on manufacturing service combination optimization based on neural network and multi-attribute decision making. Neural Comput Appl 32:1691–1700. https://doi.org/10.1007/s00521-019-04241-6
Yang X, Chen X (2020) Using a combined evaluation method to assess water resources sustainable utilization in Fujian Province, China. Environ Dev Sustain. https://doi.org/10.1007/s10668-020-00939-z
Yucesan M, Mete S, Serin F, Celik E, Gul M (2019) An integrated best-worst and interval type-2 fuzzy TOPSIS methodology for green supplier selection. Mathematics (Basel) 7:182. https://doi.org/10.3390/math7020182
Zhang F, Liu Z (2017) Combined evaluation methods: a literature review. J Syst Eng 32:557–569
Zhao K (2008) The theoretical basis and basic algorithm of binary connection A +Bi and its application in AI. CAAI Trans Intell Syst 3:476–486
Zhao K (2010) Decision making algorithm based on set par analysis for use when facing multiple uncertain in attributes. CAAI Trans Intell Syst 5:41–50
Zhou H, Wang J, Zhang H (2019) Stochastic multicriteria decision-making approach based on SMAA-ELECTRE with extended gray numbers. Int Trans Oper Res 26:2032–2052. https://doi.org/10.1111/itor.12380
Acknowledgements
This work was supported by the Fundamental Research Funds for the Universities of Henan Province (Grant no. SKJZD2021-02). The authors are grateful to the anonymous referees for their comments and suggestions for improving the quality of this paper.
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Ma, J., Yuan, Z., Zheng, G. et al. Combination Generalized Grey Target Decision Method for Mixed Attributes Based on Zero-Sum Game Theory. Group Decis Negot 31, 1121–1143 (2022). https://doi.org/10.1007/s10726-022-09794-x
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DOI: https://doi.org/10.1007/s10726-022-09794-x