Skip to main content

Advertisement

SpringerLink
Log in

Some Maclaurin symmetric mean aggregation operators based on two-dimensional uncertain linguistic information and their application to decision making

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

Abstract

The Maclaurin symmetric mean (MSM) operator has the characteristic of capturing the interrelationship among the multi-input arguments. The two-dimensional uncertain linguistic variables (2DULVs) add a subjective evaluation on the reliability of the evaluation results given by decision makers, so they can better express fuzzy information, and the improved operational laws of 2DULVs can avoid omitting information and make the operations more accurate. In order to fully take the advantages of the MSM operator and the improved operational laws of the 2DULVs, in this paper, we extend the MSM operator to the environment of 2DULVs, and two new aggregated operators are proposed, including the MSM operator for 2DULVs (2DULMSM) and the weighted MSM operator for 2DULVs (W2DULMSM). Simultaneously, we discuss some desirable properties and special cases with respect to different parameter values in these operators. Further, based on W2DULMSM operator, an approach to multiple-attribute group decision-making problems with 2DULVs is developed. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods.

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

Similar content being viewed by others

References

  1. Abu-Saris R, Hajja M (2006) On Gauss compounding of symmetric weighted arithmetic means. J Math Anal Appl 322:729–734

    Article  MathSciNet  MATH  Google Scholar 

  2. Anisseh M, Piri F, Shahraki MR (2012) Fuzzy extension of TOPSIS model for group decision making under multiple criteria. Artif Intell Rev 38(4):325–338

    Article  Google Scholar 

  3. Bapat RB (1993) Symmetrical function means and permanents. Linear Algebra Appl 182:101–108

    Article  MathSciNet  MATH  Google Scholar 

  4. Cuttler A, Greene C, Skandera M (2011) Inequalities for symmetric means. Eur J Comb 32:745–761

    Article  MathSciNet  MATH  Google Scholar 

  5. Deli I (2017) Interval-valued neutrosophic soft sets and its decision making. Int J Mach Learn Cybernet 8(2):665–676

    Article  MathSciNet  Google Scholar 

  6. Deli I (2015) npn-Soft sets theory and applications. Ann Fuzzy Math inform 10(6):847–862

    MathSciNet  MATH  Google Scholar 

  7. Detemple D, Robertson J (1979) On generalized symmetric means of two variables. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 634 677, pp 236–238

  8. Gao P (2008) On a conjecture on the symmetric means. J Math Anal Appl 337:416–424

    Article  MathSciNet  MATH  Google Scholar 

  9. He X (2017) Climate change adaptation approaches with nomadic culture characteristics in Inner Mongolia grassland in China. Chin J Popul Resour Environ 15(3):220–225

    Article  Google Scholar 

  10. Lee M, Tarokh M, Cross M (2010) Fuzzy logic decision making for multi-robot security systems. Artif Intell Rev 34(2):177–194

    Article  Google Scholar 

  11. Liu P (2013) Some geometric aggregation operators based interval valued intuitionistic uncertain linguistic variables and their application to group decision making. Appl Math Model 37:2430–2444

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu P (2017) Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators. Comput Ind Eng 108:199–212

    Article  Google Scholar 

  13. Liu P, Chen SM (2018) Multiattribute group decision making based on intuitionistic 2-tuple linguistic information. Inf Sci 430–431:599–619

    Article  MathSciNet  Google Scholar 

  14. Liu P, Chen SM (2017) Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Trans Cybern 47(9):2514–2530

    Article  Google Scholar 

  15. Liu P, Chen SM, Liu J (2017) Some intuitionistic fuzzy interaction partitioned Bonferroni mean operators and their application to multi-attribute group decision making. Inf Sci 411:98–121

    Article  Google Scholar 

  16. Liu P, Chu Y (2015) Some two-dimensional uncertain linguistic Heronian mean operators and their application in multiple-attribute decision making. Neural Comput Appl 26:1461–1480

    Article  Google Scholar 

  17. Liu P, He L, Yu X (2016) Generalized hybrid aggregation operators based on the 2-dimension uncertain linguistic information for multiple attribute group decision making. Group Decis Negot 25:103–126

    Article  Google Scholar 

  18. Liu P, Jin F (2012) Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Inf Sci 205:58–71

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu P, Li H (2017) Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making. Cogn Comput 9(4):494–512

    Article  Google Scholar 

  20. Liu P, Liu J, Merigó JM (2018) Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making. Appl Soft Comput 62:395–422

    Article  Google Scholar 

  21. Liu P, Qi X (2014) Some generalized dependent aggregation operators with 2-dimension linguistic information and their application to group decision making. J Intell Fuzzy Syst 27:1761–1773

    MathSciNet  MATH  Google Scholar 

  22. Liu P, Shi L (2017) Some neutrosophic uncertain linguistic number Heronian mean operators and their application to multi-attribute group decision making. Neural Comput Appl 28(5):1079–1093

    Article  Google Scholar 

  23. Liu P, Tang G (2016) Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cogn Comput 8(6):1036–1056

    Article  Google Scholar 

  24. Liu P, Wang Y (2016) The aggregation operators based on the 2-dimension uncertain linguistic information and their application to decision making. Int J Mach Learn Cybern 7(6):1057–1074

    Article  Google Scholar 

  25. Liu P, Wang P (2017) Some improved linguistic intuitionistic fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Inf Technol Decis Mak 16(3):817–850

    Article  Google Scholar 

  26. Liu P, Zhang X (2012) An approach to group decision making based on 2-dimension uncertain linguistic assessment information. Technol Econ Dev Econ 18(3):424–437

    Article  Google Scholar 

  27. Liu ZM, Liu PD (2015) Multi-criteria decision making method based on two-dimensional fuzzy information and application research. Research report of the humanities and social sciences research project of ministry of education of China, pp 54–65 (In Chinese)

  28. Ma X, Liu Q, Zhan J (2016) A survey of decision making methods based on certain hybrid soft set models. Artif Intell Rev. https://doi.org/10.1007/s10462-016-9490-x

    Article  Google Scholar 

  29. Maclaurin C (1729) A second letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans R Soc Lond Ser A 36:59–96

    Google Scholar 

  30. Qin JD, Liu XW (2014) An approach to intuitionistic fuzzy multipleattribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst 27(5):2177–2190

    MATH  Google Scholar 

  31. Sun BZ, Ma WM (2014) Soft fuzzy rough sets and its application in decision making. Artif Intell Rev 41(1):67–80

    Article  Google Scholar 

  32. Wang JQ, Li JJ (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Sci Technol Inf 33:8–9

    Google Scholar 

  33. Xu ZS (2004) Uncertain multiple attribute decision making methods and application. Tsinghua University Press, Beijing

    Google Scholar 

  34. Xu ZS (2006) Induced uncertain linguistic OWA operators applied to group decision making. Inf Fusion 7(2):231–238

    Article  MathSciNet  Google Scholar 

  35. Xu ZS (2007) Group decision making with triangular fuzzy linguistic variables. Intell Data Eng Autom Learn IDEAL 4881:17–26

    Google Scholar 

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

    Article  Google Scholar 

  37. Yu DJ, Wu YY (2012) Interval-valued intuitionistic fuzzy Heronian mean operators and their application in multi-criteria decision making. Afr J Bus Manage 6(11):4158–4168

    Google Scholar 

  38. Yu X, Xu M, Ding Y (2017) Carbon emissions of china’s industrial sectors based on input–output analysis. Chin J Popul Resour Environ 15(2):147–156

    Article  Google Scholar 

  39. Yu XH, Xu ZS, Liu SS, Chen Q (2012) Multi-criteria decision making with 2-dimension linguistic aggregation techniques. Int J Intell Syst 27(6):539–562

    Article  Google Scholar 

  40. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning—I. Inf Sci 8:199–249

    Article  MathSciNet  MATH  Google Scholar 

  41. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning—II. Inf Sci 8:301–357

    Article  MathSciNet  MATH  Google Scholar 

  42. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning—III. Inf Sci 9:43–80

    Article  MathSciNet  MATH  Google Scholar 

  43. Zhang B, He M, Pan H (2017) A study on the design of a hybrid policy for carbon abatement. Chin J Popul Resour Environ 15(1):50–57

    Article  Google Scholar 

  44. Zhang C, Zhou GZ, Zhu WD (2011) Research on peer review system for the national science foundation based on two-dimensional semantics evidence reasoning. China Soft Sci 2:176–182

    Google Scholar 

  45. Zhang X, Liu PD, Wang YM (2015) Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators. J Intell Fuzzy Syst 29(5):2235–2246

    Article  MathSciNet  MATH  Google Scholar 

  46. Zhang XM, Haining Z (2007) S-geometric convexity of a function involving Maclaurin’s elementary symmetric mean. J Inequal Pure Appl Math 8:156–165

    MathSciNet  Google Scholar 

  47. Zhang ZH, Xiao ZG, Srivastava HM (2009) A general family of weighted elementary symmetric means. Appl Math Lett 22:24–30

    Article  MathSciNet  MATH  Google Scholar 

  48. Zhu WD, Zhou GZ, Yang SL (2009) An approach to group decision making based on 2-dimension linguistic assessment information. Syst Eng 27(2):113–118

    Google Scholar 

  49. Zhu J (2017) The 2030 agenda for sustainable development and China’s implementation. Chin J Popul Resour Environ 15(2):142–146

    Article  Google Scholar 

Download references

Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Nos. 71771140, 71471172), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), Shandong Provincial Social Science Planning Project (Nos. 17BGLJ04,16CGLJ31 and 16CKJJ27), the Natural Science Foundation of Shandong Province (No. ZR2017MG007), the Teaching Reform Research Project of Undergraduate Colleges and Universities in Shandong Province (No. 2015Z057) and Key research and development program of Shandong Province (No. 2016GNC110016). The authors also would like to express appreciation to the anonymous reviewers and Editors for their very helpful comments that improved the paper.

Author information

Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan Shandong, 250014, China

    Peide Liu & Ying Li

  2. Department of Development Planning and Discipline Construction, Shandong Normal University, Jinan Shandong, 250013, China

    Maocong Zhang

Authors
  1. Peide Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maocong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peide Liu.

Ethics declarations

Conflict of interest

We declare that we do have no commercial or associative interests that represent a conflict of interests in connection with this manuscript. There are no professional or other personal interests that can inappropriately influence our submitted work.

Research involving human participants and/or animals

This article does not contain any studies with human participants or animals performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, P., Li, Y. & Zhang, M. Some Maclaurin symmetric mean aggregation operators based on two-dimensional uncertain linguistic information and their application to decision making. Neural Comput & Applic 31, 4305–4318 (2019). https://doi.org/10.1007/s00521-018-3350-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-018-3350-3

Keywords

Search

Navigation