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Multi-criteria group decision-making methods based on new intuitionistic fuzzy Einstein hybrid weighted aggregation operators

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Abstract

Intuitionistic fuzzy sets (IFSs) are a very efficient tool to depict uncertain or fuzzy information. In the course of decision making with IFSs, intuitionistic fuzzy aggregation operators play a very important role which has received more and more attention in recent years. This paper proposes a family of intuitionistic fuzzy Einstein hybrid weighted operators, including the intuitionistic fuzzy Einstein hybrid weighted averaging operator, the intuitionistic fuzzy Einstein hybrid weighted geometric operator, the quasi-intuitionistic fuzzy Einstein hybrid weighted averaging operator, and the quasi-intuitionistic fuzzy Einstein hybrid weighted geometric operator. All these newly developed operators not only can weight both the intuitionistic fuzzy arguments and their ordered positions simultaneously but also have some desirable properties, such as idempotency, boundedness, and monotonicity. Based on these proposed operators, two algorithms are given to solve multi-criteria single-person decision making and multi-criteria group decision making with intuitionistic fuzzy information, respectively. Two numerical examples are provided to illustrate the practicality and validity of the proposed methods and aggregation operators.

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References

  1. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen SM, Tan JM (1994) Handling multicriteria fuzzy decisionmaking problems based on vague set theory. Fuzzy Sets Syst 67:163–172

    Article  MATH  Google Scholar 

  3. Choquet G (1954) Theory of capacities. Ann Inst Fourier 5:131–295

    Article  MathSciNet  MATH  Google Scholar 

  4. Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38(2):325–339

    Article  MathSciNet  MATH  Google Scholar 

  5. Deschrijver G, Kerre E (2002) A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms. Notes Intuit Fuzzy Sets 8(1):19–27

    MATH  Google Scholar 

  6. Dyckhoff H, Pedrycz W (1984) Generalized means as model of compensative connectives. Fuzzy Sets Syst 14(2):143–154

    Article  MathSciNet  MATH  Google Scholar 

  7. Fodor J, Marichal JL, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3:236–240

    Article  Google Scholar 

  8. Hájek P (1998) Metamathematics of fuzzy logic. Kluwer, Dordrecht

    Book  MATH  Google Scholar 

  9. Hardy GH, Littlewood JE, Pólya G (1934) Inequalities. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  10. Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 14:103–113

    Article  MATH  Google Scholar 

  11. Klement EP, Mesiar R, Pap E (2004) Triangular norms. Position paper I: basic analytical and algebraic properties. Fuzzy Sets Syst 143(1):5–26

    Article  MathSciNet  MATH  Google Scholar 

  12. Liao HC, Xu ZS (2014) Intuitionistic fuzzy hybrid weighted aggregation operators. Int J Intell Syst 29(11):971–993

    Article  Google Scholar 

  13. Lin J, Jiang Y (2014) Some hybrid weighted averaging operators and their application to decision making. Inf Fusion 16:18–28

    Article  Google Scholar 

  14. Qin JD, Liu XW (2014) An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst 27:2177–2190

    MathSciNet  MATH  Google Scholar 

  15. Tan CQ, Chen XH (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37(1):149–157

    Article  Google Scholar 

  16. Wang W, Liu X (2012) Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans Fuzzy Syst 20:923–938

    Article  Google Scholar 

  17. Wang WZ, Liu XW (2011) Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int J Intell Syst 26:1049–1075

    Article  Google Scholar 

  18. Wang TC, Lee HD (2009) Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert Syst Appl 36:8980–8985

    Article  Google Scholar 

  19. Wang YM, Yang JB, Xu DL (2005) Interval weight generation approaches based on consistency test and interval comparison matrices. Appl Math Comput 167:252–273

    MathSciNet  MATH  Google Scholar 

  20. Wei G (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10(2):423–431

    Article  MathSciNet  Google Scholar 

  21. Xia MM, Xu ZS (2010) Generalized point operators for aggregating intuitionistic fuzzy information. Int J Intell Syst 25(11):1061–1080

    MATH  Google Scholar 

  22. Xia MM, Xu ZS, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowl-Based Syst 31:78–88

    Article  Google Scholar 

  23. Xia MM, Xu ZS, Zhu B (2012) Generalized intuitionistic fuzzy Bonferroni means. Int J Intell Syst 27:23–47

    Article  Google Scholar 

  24. Xia MM, Xu ZS, Zhu B (2013) Geometric Bonferroni means with their application in multi-criteria decision making. Knowl Based Syst 40:88–100

    Article  Google Scholar 

  25. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187

    Article  Google Scholar 

  26. Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180(5):726–736

    Article  MathSciNet  MATH  Google Scholar 

  27. Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl Based Syst 24(6):749–760

    Article  Google Scholar 

  28. Xu ZS, Cai X (2010) Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optim Decis Making 9(4):359–381

    Article  MathSciNet  MATH  Google Scholar 

  29. Xu ZS, Xia MM (2011) Induced generalized intuitionistic fuzzy operators. Knowl-Based Syst 24(2):197–209

    Article  Google Scholar 

  30. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433

    Article  MathSciNet  MATH  Google Scholar 

  31. Xu ZS, Yager RR (2008) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason 48(1):246–262

    Article  MATH  Google Scholar 

  32. Xu ZS, Yager RR (2011) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cybern B Cybern 41(2):568–578

    Article  Google Scholar 

  33. Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18:183–190

    Article  MATH  Google Scholar 

  34. Yager RR, Filev DP (1999) Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern B Cybern 29(2):141–150

    Article  Google Scholar 

  35. Yu DJ (2013) Intuitionistic fuzzy geometric Heronian mean aggregation operators. Appl Soft Comput 13(2):1235–1246

    Article  Google Scholar 

  36. Yu DJ (2014) Intuitionistic fuzzy information aggregation under confidence levels. Appl Soft Comput 19:147–160

    Article  Google Scholar 

  37. Yu XH, Xu ZS (2013) Prioritized intuitionistic fuzzy aggregation operators. Inf Fusion 14:108–116

    Article  Google Scholar 

  38. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  39. Zhang ZM (2013) Generalized Atanassov’s intuitionistic fuzzy power geometric operators and their application to multiple attribute group decision making. Inf Fusion 14(4):460–486

    Article  Google Scholar 

  40. Zhao XF, Lin R, Zhang Y (2014) Intuitionistic fuzzy heavy aggregating operators and their application to strategic decision making problems. J Intell Fuzzy Syst 26(6):3065–3074

    MathSciNet  MATH  Google Scholar 

  41. Zhao XF, Wei GW (2013) Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowl-Based Syst 37:472–479

    Article  Google Scholar 

  42. Zhao H, Xu ZS, Ni M, Liu S (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30

    Article  MATH  Google Scholar 

  43. Zhao H, Xu ZS, Yao ZQ (2014) Intuitionistic fuzzy density-based aggregation operators and their applications to group decision making with intuitionistic preference relations. Int J Uncertain Fuzziness Knowl Based Syst 22(1):145–169

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The author thanks the anonymous referees for their valuable suggestions in improving this paper. This work is supported by the National Natural Science Foundation of China (Grant No. 61375075), the Natural Science Foundation of Hebei Province of China (Grant No. F2012201020) and the Scientific Research Project of Department of Education of Hebei Province of China (Grant No. QN2016235).

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  1. College of Mathematics and Information Science, Hebei University, Baoding, 071002, Hebei Province, People’s Republic of China

    Zhiming Zhang

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  1. Zhiming Zhang
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Zhang, Z. Multi-criteria group decision-making methods based on new intuitionistic fuzzy Einstein hybrid weighted aggregation operators. Neural Comput & Applic 28, 3781–3800 (2017). https://doi.org/10.1007/s00521-016-2273-0

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  • DOI: https://doi.org/10.1007/s00521-016-2273-0

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