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Some new Shapley 2-tuple linguistic Choquet aggregation operators and their applications to multiple attribute group decision making

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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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References

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Belles-Sampera J, Merigó JM, Guillén M, Santolino M (2014) Indicators for the characterization of discrete Choquet integrals. Inf Sci 267:201–216

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Chen ZP, Yang W (2011) A new multiple attribute group decision making method in intuitionistic fuzzy setting. Appl Math Model 35(9):4424–4437

    Article  MathSciNet  MATH  Google Scholar 

  • Choquet G (1953) Theory of capacities. Annales de l’institut Fourier 5:131–295

    Article  MathSciNet  MATH  Google Scholar 

  • Delgado M, Verdegay JL, Vila MA (1992) Linguistic decision making models. Int J Intel Syst 7:479–492

    Article  MATH  Google Scholar 

  • Grabisch M (1995) Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst 69:279–298

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    MATH  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Meng FY, Zhang Q (2014) Induced continuous Choquet integral operators and their application to group decision making. Comput Ind Eng 68:42–53

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • Merigó JM, Gil-Lafuente AM (2013) Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Inf Sci 236:1–16

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  MathSciNet  Google Scholar 

  • Wakker P (1999) Additive representations of preferences: a new foundation of decision analysis. Springer, Berlin

    MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Wang YM (1998) Using the method of maximizing deviations to make decision for multi-indices. J Syst Eng Electron 7(3):24–26

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180:726–736

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS, Xia MM (2011) Induced generalized intuitionistic fuzzy operators. Knowl Based Syst 24:197–209

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang ZH, Wei FJ, Zhou SH (2015) Approaches to comprehensive evaluation with 2-tuple linguistic information. J Intell Fuzzy Syst 28(1):469–475

    MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

Download references

Acknowledgments

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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Authors and Affiliations

  1. School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, China

    Yanbing Ju & Xiaoyue Liu

  2. Graduate School of Education, Peking University, Beijing, 100871, China

    Aihua Wang

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  1. Yanbing Ju
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  2. Xiaoyue Liu
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  3. Aihua Wang
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Correspondence to Yanbing Ju.

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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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