Abstract
In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with 2-tuple linguistic information. Firstly, motivated by the ideas of Choquet integral and Shapley index, we propose three 2-tuple linguistic aggregation operators called Shapley 2-tuple linguistic Choquet averaging operator, Shapley 2-tuple linguistic Choquet geometric operator and generalized Shapley 2-tuple linguistic Choquet averaging operator. Then we discuss some properties of these operators, such as idempotency, monotonicity, boundary and commutativity. Secondly, if the information about the weights of decision makers (DMs) and attributes is incompletely known, we build two models to determine the optimal fuzzy measures on DM set and attribute set, respectively. Furthermore, we develop a new method for multiple attribute group decision making under 2-tuple linguistic environment based on the proposed operators. Finally, we apply the developed MAGDM method to select the most desirable emergency alternative and the validity of the developed method is verified by comparing the evaluation results with those obtained from the existing 2-tuple correlated aggregation operators.
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Angilella S, Corrente S, Greco S (2015) Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem. Eur J Oper Res 240:172– 182
Ashayeri J, Tuzkaya G, Tuzkaya UR (2012) Supply chain partners and configuration selection: an intuitionistic fuzzy Choquet integral operator based approach. Expert Syst Appl 39(3):3642–3649
Belles-Sampera J, Merigó JM, Guillén M, Santolino M (2014) Indicators for the characterization of discrete Choquet integrals. Inf Sci 267:201–216
Bonetti A, Bortot S, Fedrizzi F, Marques Pereira RA, Molinari A (2010) Modelling group processes and effort estimation in project management using the Choquet integral: an MCDM approach. Expert Syst Appl 39(18):13366–13375
Chen ZP, Yang W (2011) A new multiple attribute group decision making method in intuitionistic fuzzy setting. Appl Math Model 35(9):4424–4437
Choquet G (1953) Theory of capacities. Annales de l’institut Fourier 5:131–295
Delgado M, Verdegay JL, Vila MA (1992) Linguistic decision making models. Int J Intel Syst 7:479–492
Grabisch M (1995) Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst 69:279–298
Herrera F, Herrera-Viedma E, Verdegay JL (1996) Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets Syst 79:175–190
Herrera F, Herrera-Viedma E, Verdegay JL (1997) A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets Syst 88:31–49
Herrera F, Martínez L (2000a) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752
Herrera F, Martínez L (2000b) An approach for combining linguistic and numerical information based on 2-tuple fuzzy representation model in decision making. Int J Uncertain Fuzz Knowl-Based Syst 8(5):539–562
Herrera F, Martínez L (2001) A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision making. IEEE Trans Syst Man Cybern B 31:227–234
Jiang XP, Wei GW (2014) Some Bonferroni mean operators with 2-tuple linguistic information and their application to multiple attribute decision making. J Intell Fuzzy Syst 27(5):2153–2162
Ju YB (2014) A new method for multiple criteria group decision making with incomplete weight information under linguistic environment. Appl Math Model 38(21–22):5256–5268
Ju YB, Wang AH (2012) Emergency alternative evaluation under group decision makers: A method of incorporating DS/AHP with extended TOPSIS. Expert Syst Appl 39(1):1315–1323
Ju YB, Wang AH (2013) Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting. Appl Math Model 37(20–21):9031–9040
Ju YB, Yang SH (2014a) A new method for multiple attribute group decision-making with intuitionistic trapezoid fuzzy linguistic information. Soft Comput. doi: 10.1007/s00500-014-1403-9
Ju YB, Yang SH (2014b) Approaches for multi-attribute group decision making based on intuitionistic trapezoid fuzzy linguistic power aggregation operators. J Intell Fuzzy Syst 27(2):987–1000
Ju YB, Yang SH, Liu XY (2014) A novel method for multiattribute decision making with dual hesitant fuzzy triangular linguistic information. J Appl Math. doi:10.1155/2014/909823
Li CG, Zeng SZ, Pan TJ, Zheng LN (2014) A method based on induced aggregation operators and distance measures to multiple attribute decision making under 2-tuple linguistic environment. J Comput Syst Sci 80(7):1339–1349
Liao XW, Li Y, Lu B (2007) A model for selecting an ERP system based on linguistic information processing. Inf Syst 32(7):1005–1017
Liu PD (2013) Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making. Appl Math Model 37(4):2430–2444
Liu XY, Ju YB, Yang SH (2014a) Hesitant intuitionistic fuzzy linguistic aggregation operators and their applications to multiple attribute decision making. J Intell Fuzzy Syst 27(3):1187–1201
Liu XY, Ju YB, Yang SH (2014b) Some generalized interval-valued hesitant uncertain linguistic aggregation operators and their applications to multiple attribute group decision making. Soft Comput. doi: 10.1007/s00500-014-1518-z
Marichal JL (2000) The influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making. Discrete Appl Math 107(1–3):139–164
Meng FY, Zhang Q (2014) Induced continuous Choquet integral operators and their application to group decision making. Comput Ind Eng 68:42–53
Meng FY, Zhang Q, Cheng H (2013) Approaches to multiple-criteria group decision making based on interval-valued intuitionistic fuzzy Choquet integral with respect to the generalized \(\lambda \)-Shapley index. Knowl Based Syst 37:237–249
Meng FY, Chen XH, Zhang Q (2014) Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making. Appl Math Model 38(9–10):2543–2557
Meng FY, Chen XH, Zhang Q (2015) Induced generalized hesitant fuzzy Shapley hybrid operators and their application in multi-attribute decision making. Appl Soft Comput 28:599–607
Merigó JM, Gil-Lafuente AM (2013) Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Inf Sci 236:1–16
Merigó JM, Casanovas M, Martínez L (2010) Linguistic aggregation operators for linguistic decision making based on the Dempster-Shafer theory of evidence. Int J Uncertainty Fuzziness Knowl Based Syst 18(3):287–304
Park JH, Park JM, Kwun YC (2013) 2-Tuple linguistic harmonic operators and their applications in group decision making. Knowl Based Syst 44:10–19
Shapley LS (1953) A value for n-person game. In: Kuhn H, Tucker A (eds) Contributions to the Theory of Games. Princeton University Press, Princeton
Sugeno M (1974) Theory of fuzzy integral and its application. Doctorial Dissertation, Tokyo Institute of Technology
Tai WS, Chen CT (2009) A new evaluation model for intellectual capital based on computing with linguistic variable. Expert Syst Appl 36(2):3483–3488
Wakker P (1999) Additive representations of preferences: a new foundation of decision analysis. Springer, Berlin
Wang JQ, Lu P, Zhang HY, Chen XH (2014) Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information. Inf Sci 274:177–191
Wang YM (1998) Using the method of maximizing deviations to make decision for multi-indices. J Syst Eng Electron 7(3):24–26
Wei GW (2011) Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making. Comput Ind Eng 61(1):32–38
Wei GW, Zhao XF (2012) Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making. Expert Syst Appl 39(5):5881–5886
Wu J, Liu YJ (2013) An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers. Comput Ind Eng 66(2):311–324
Xu YJ, Merigó JM, Wang HM (2102) Linguistic power aggregation operators and their application to multiple attribute group decision making. Appl Math Model 36(11):5427–5444
Xu YJ, Huang L (2008) An approach to group decision making problems based on 2-tuple linguistic aggregation operators. In: 2008 ISECS international colloquium on computing, communication, control, and management, pp 73–77
Xu YJ, Wang HM (2011) Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment. Appl Soft Comput 11(5):3988–3997
Xu ZS (2004) EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int J Uncertainty Fuzziness Knowl Based Syst 12:791–810
Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180:726–736
Xu ZS, Xia MM (2011) Induced generalized intuitionistic fuzzy operators. Knowl Based Syst 24:197–209
Yang W, Chen ZP (2012) New aggregation operators based on the Choquet integral and 2-tuple linguistic information. Expert Syst Appl 39(3):2662–2668
Zhang HM (2013) Some interval-valued 2-tuple linguistic aggregation operations and application in multiattribute group decision making. Appl Math Model 37(6):4269–4282
Zhang ZH, Wei FJ, Zhou SH (2015) Approaches to comprehensive evaluation with 2-tuple linguistic information. J Intell Fuzzy Syst 28(1):469–475
Zhang ZM (2014) 2-Tuple prioritized aggregation operators and their application to multiple attribute group decision making. Br J Math Comput Sci 4(16):2278–2297
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This research is supported by Program for New Century Excellent Talents in University (NCET-13-0037), Humanities and Social Sciences Foundation of Ministry of Education of China (No.14YJA630019).
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Communicated by V. Loia.
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Ju, Y., Liu, X. & Wang, A. Some new Shapley 2-tuple linguistic Choquet aggregation operators and their applications to multiple attribute group decision making. Soft Comput 20, 4037–4053 (2016). https://doi.org/10.1007/s00500-015-1740-3
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DOI: https://doi.org/10.1007/s00500-015-1740-3