Skip to main content

Interval Type-2 Fuzzy Aggregation Operations Based on Maclaurin Means and Its Extensions

  • Chapter
  • First Online:

Part of the book series: Uncertainty and Operations Research ((UOR))

Abstract

Maclaurin symmetric mean (MSM) (Maclaurin 1729) is a classic generalized symmetric mean, which can be regarded as an extension of Bonferroni mean (Bonferroni 1950).

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Bonferroni C (1950) Sulle medie multiple di potenze. Boll dell’Unione Matematica Italiana 5(3–4):267–270

    MathSciNet  MATH  Google Scholar 

  • Gong Y, Hu N, Zhang J, Liu G, Deng J (2015) Multi-attribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers. Comput Ind Eng 81:167–176

    Article  Google Scholar 

  • Jiang WD (2007) Some properties of dual form of the Hamy’s symmetric function. J Math Inequal 1(1):117–125

    Article  MathSciNet  Google Scholar 

  • Karnik NN, Mendel JM (2001) Centroid of a type-2 fuzzy set. Inf Sci 132(1):195–220

    Article  MathSciNet  Google Scholar 

  • Liu X, Mendel JM (2011) Connect Karnik-Mendel algorithms to root-finding for computing the centroid of an interval type-2 fuzzy set. IEEE Trans Fuzzy Syst 19(4):652–665

    Article  Google Scholar 

  • Liu X, Mendel JM, Wu D (2012) Study on enhanced Karnik-Mendel algorithms: Initialization explanations and computation improvements. Inf Sci 184(1):75–91

    Article  MathSciNet  Google Scholar 

  • Liu X, Wang YM (2013) An analytical solution method for the generalized fuzzy weighted average problem. Int J Uncertainty Fuzziness Knowl Based Syst 21(3):455–480

    Article  MathSciNet  Google Scholar 

  • Maclaurin C (1729) A second letter to Martin Folkes, Esq.; concerning the roots of equations, with the demonstartion of other rules in algebra. Phil. Transactions 36:59

    Google Scholar 

  • Merigó JM, Gil-Lafuente AM, Martorell O (2012) Uncertain induced aggregation operators and its application in tourism management. Expert Syst Appl 39(1):869–880

    Article  Google Scholar 

  • Pedrycz W, Song M (2014) A granulation of linguistic information in AHP decision-making problems. Inf Fusion 17:93–101

    Article  Google Scholar 

  • Qin JD, Liu XW (2015) Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment. Inf Sci 297:293–315

    Article  MathSciNet  Google Scholar 

  • Spearman C (1987) The proof and measurement of association between two things. Am J Psychol 100(3–4):441–471

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zhu B, Xu ZS (2013) Hesitant fuzzy Bonferroni means for multi-criteria decision making. J Oper Res Society 64(12):1831–1840

    Article  Google Scholar 

  • Zhu B, Xu ZS, Xia MM (2012) Hesitant fuzzy geometric Bonferroni means. Inf Sci 205:72–85

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jindong Qin .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Qin, J., Liu, X. (2019). Interval Type-2 Fuzzy Aggregation Operations Based on Maclaurin Means and Its Extensions. In: Type-2 Fuzzy Decision-Making Theories, Methodologies and Applications. Uncertainty and Operations Research. Springer, Singapore. https://doi.org/10.1007/978-981-13-9891-9_3

Download citation

Publish with us

Policies and ethics