Skip to main content
SpringerLink
Log in

MAGDM based on triangular Atanassov’s intuitionistic fuzzy information aggregation

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Triangular Atanassov’s intuitionistic fuzzy number (TAIFN) has better ability to model fuzzy ill-defined quantity. The information aggregation of TAIFNs is of great importance in multi-attribute group decision-making (MAGDM). In this paper, some arithmetic aggregation operators for TAIFNs are defined, with the triangular Atanassov’s intuitionistic fuzzy weighted average (TAIFWA) operator, ordered weighted average (TAIFOWA) operator and hybrid weighted average (TAIFHWA) operator included. Then we further investigate the Atanassov’s triangular intuitionistic fuzzy generalized ordered weighted average (TAIFGOWA) operator and generalized hybrid weighted average (TAIFGHWA) operator. Some desirable and useful properties of these operators, such as idempotence, monotonicity and boundedness, are also discussed. For the MAGDM with TAIFNs and incomplete attribute weight information, a multi-objective programming model is constructed by minimizing total deviation between all alternatives and fuzzy positive ideal solution, which is transformed into a linear goal programming. Consequently, the attribute weights are objectively derived. Thereby, an innovated MAGDM method is proposed on the basis of the TAIFWA and TAIFGHWA operators. Finally, a green supplier selection example is provided to illuminate the practicability of the proposed method in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Wan SP, Li DF (2015) Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees. Inf Sci 325:484–503

    Article  MathSciNet  Google Scholar 

  3. Wan SP, Dong JY (2015) Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees. Inf Fusion 26:49–65

    Article  Google Scholar 

  4. Wan SP, Li DF (2014) Atanassov’s intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov’s intuitionistic fuzzy truth degrees. IEEE Trans Fuzzy Syst 22(2):300–312

    Article  MathSciNet  Google Scholar 

  5. Wan SP, Dong JY (2014) A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making. J Comput Syst Sci 80(1):237–256

    Article  MathSciNet  MATH  Google Scholar 

  6. Shu MH, Cheng CH, Chang JR (2006) Using intuitionistic fuzzy sets for fault tree analysis on printed circuit board assembly. Microelectron Reliab 46(12):2139–2148

    Article  Google Scholar 

  7. Li DF (2008) A note on “using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly”. Microelectron Reliab 48(10):1741

    Article  Google Scholar 

  8. Nan JX, Li DF, Zhang MJ (2010) A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers. Int J Comput Intell Syst 3(3):280–289

    Article  Google Scholar 

  9. Li DF (2010) A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. Comput Math Appl 60(6):1557–1570

    Article  MathSciNet  MATH  Google Scholar 

  10. Li DF, Nan JX, Zhang MJ (2010) A ranking method of triangular intuitionistic fuzzy numbers and application to decision making. Int J Comput Intell Syst 3(5):522–530

    Article  Google Scholar 

  11. Wan SP, Wang QY, Dong JY (2013) The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers. Knowl-Based Syst 52:65–77

    Article  Google Scholar 

  12. Wan SP, Li DF, Rui ZF (2013) Possibility mean, variance and covariance of triangular intuitionistic fuzzy numbers. J Intell Fuzzy Syst 24(4):847–858

    MathSciNet  MATH  Google Scholar 

  13. Wan SP (2013) Multi-attribute decision making method based on possibility variance coefficient of triangular intuitionistic fuzzy numbers. Int J Uncertain Fuzziness Knowl-Based Syst 21(2):223–243

    Article  MathSciNet  MATH  Google Scholar 

  14. Wan SP, Dong JY (2014) Possibility method for triangular intuitionistic fuzzy multi-attribute group decision making with incomplete weight information. Int J Comput Intell Syst 7(1):65–79

    Article  MathSciNet  Google Scholar 

  15. Wang JQ, Nie RR, Zhang HY, Chen XH (2013) New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis. Inf Sci 251:79–95

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang JQ (2008) Overview on fuzzy multi-criteria decision-making approach. Control Decis 23(6):601–607

    MathSciNet  MATH  Google Scholar 

  17. Wang JQ, Zhang Z (2009) Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. J Syst Eng Electron 20(2):321–326

    MathSciNet  Google Scholar 

  18. Dong JY, Yang DY, Wan SP (2015) Trapezoidal intuitionistic fuzzy prioritized aggregation operators and application to multi-attribute decision making. Iran J Fuzzy Syst 12(4):1–32

    MathSciNet  MATH  Google Scholar 

  19. Wan SP, Dong JY (2010) Method of intuitionistic trapezoidal fuzzy number for multi-attribute group decision. Control Decis 25(5):773–776

    MathSciNet  Google Scholar 

  20. Yue J (2011) Expected value method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems. Expert Syst Appl 38(9):11730–11734

    Article  Google Scholar 

  21. Wan SP, Dong JY (2015) Power geometric operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making. Appl Soft Comput 29:153–168

    Article  Google Scholar 

  22. Wan SP (2013) Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making. Appl Math Model 37(6):4112–4126

    Article  MathSciNet  MATH  Google Scholar 

  23. Wu J, Cao QW (2012) Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl Math Model 37:318–327

    Article  MathSciNet  MATH  Google Scholar 

  24. Wan SP (2011) Multi-attribute decision making method based on interval intuitionistic trapezoidal fuzzy number. Control Decis 26(6):857–861

    MathSciNet  MATH  Google Scholar 

  25. Wan SP (2012) Method based on fractional programming for interval-valued intuitionistic trapezoidal fuzzy number multi-attribute decision making. Control Decis 27(3):455–458

    MathSciNet  Google Scholar 

  26. Wu J, Liu YJ (2013) An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers. Comput Ind Eng 66:311–324

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. Yager RR (2004) Generalized OWA aggregation operators. J Fuzzy Optim Decis Mak 3(1):93–107

    Article  MathSciNet  MATH  Google Scholar 

  29. Merigó JM, Casanovas M (2010) The fuzzy generalized OWA operator and its application in strategic decision making. Cybern Syst 41(5):359–370

    Article  Google Scholar 

  30. Xu ZS, Da QL (2003) An overview of operators for aggregating information. Int J Intell Syst 18:953–969

    Article  MATH  Google Scholar 

  31. Merigó JM, Casanovas M (2010) Fuzzy generalized hybrid aggregation operators and its application in decision making. Int J Fuzzy Syst 12(1):15–24

    Google Scholar 

  32. Merigó JM, Casanovas M (2011) The uncertain induced quasi-arithmetic OWA operator. Int J Intell Syst 26(1):1–24

    Article  MATH  Google Scholar 

  33. Emrouznejad A, Marra M (2014) Ordered weighted average operators 1988–2014: a citation based literature survey. Int J Intell Syst 29:994–1014

    Article  Google Scholar 

  34. Yager RR, Kacprzyk J, Beliakov G (2011) Recent developments on the ordered weighted average operators: Theory and practice. Springer, Berlin

    Book  Google Scholar 

  35. Li DF (2011) Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information. Appl Soft Comput 11(4):3402–3418

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the National Natural Science Foundation of China (Nos. 71061006, 61263018 and 11461030), the Natural Science Foundation of Jiangxi Province of China (Nos. 20114BAB201012 and 20142BAB201011), the Science and Technology Project of Jiangxi province educational department of China (Nos. GJJ15265 and GJJ15267), Young scientists Training object of Jiangxi province (No. 20151442040081) and the Excellent Young Academic Talent Support Program of Jiangxi University of Finance and Economics.

Author information

Authors and Affiliations

  1. College of Information Technology, Jiangxi University of Finance and Economics, No. 168, Shuang-gang East Road, Economic and Technological Development District, Nanchang, 330013, China

    Shu-ping Wan & Li-Lian Lin

  2. School of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China

    Jiu-ying Dong

  3. Research Center of Applied Statistics, Jiangxi University of Finance and Economics, No. 168, Shuang-gang East Road, Economic and Technological Development District, Nanchang, 330013, China

    Jiu-ying Dong

Authors
  1. Shu-ping Wan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li-Lian Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiu-ying Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li-Lian Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wan, Sp., Lin, LL. & Dong, Jy. MAGDM based on triangular Atanassov’s intuitionistic fuzzy information aggregation. Neural Comput & Applic 28, 2687–2702 (2017). https://doi.org/10.1007/s00521-016-2196-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2196-9

Keywords

Search

Navigation