Skip to main content
SpringerLink
Log in

Intuitionistic Fuzzy Z-numbers

  • Conference paper
  • First Online:
Intelligent and Fuzzy Techniques: Smart and Innovative Solutions (INFUS 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1197))

Included in the following conference series:

Abstract

Fuzzy sets and its extensions are widely used to determine membership of an element using different functions to decrease the effect of uncertainty. In this paper, intuitionistic fuzzy Z-numbers that are a new extension of fuzzy sets are proposed for the first time. First, fuzzy Z-numbers and intuitionistic fuzzy numbers are determined as preliminaries. Then definitions and defuzzification of intuitionistic fuzzy Z-numbers are proposed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

  2. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8(3), 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  3. Sambuc, R.: Function Φ-Flous. Application a l’aide au Diagnostic en Pathologie Thyroidienne. These de Doctorat en Medicine. University of Marseille (1975)

    Google Scholar 

  4. Jahn, K.U.: Intervallwertige Mengen. Math Nach 68(1), 115–132 (1975)

    Article  Google Scholar 

  5. Grattan-Guinness, I.: Fuzzy membership mapped onto intervals and many-valued quantities. Math. Logic Q. 22(1), 149–160 (1976)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  7. Yager, R.R.: On the theory of bags. Int. J. General Syst. 13(1), 23–37 (1986)

    Article  MathSciNet  Google Scholar 

  8. Smarandache, F.: Neutrosophy. Neutrosophic Probability, set, and logic, ProQuest information & learning. Ann Arbor, Michigan, USA, vol. 105, pp. 118–123 (1998)

    Google Scholar 

  9. Garibaldi, J.M., Ozen, T.: Uncertain fuzzy reasoning: a case study in modelling expert decision making. IEEE Trans. Fuzzy Syst. 15(1), 16–30 (2007)

    Article  Google Scholar 

  10. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)

    MATH  Google Scholar 

  11. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181(14), 2923–2932 (2011)

    Article  Google Scholar 

  12. Yager, R.R., Abbasov, A.M.: Pythagorean membership grades, complex numbers, and decision making. Int. J. Intell. Syst. 28(5), 436–452 (2013)

    Article  Google Scholar 

  13. Yager, R.R.: Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 57–61. IEEE (2013)

    Google Scholar 

  14. Cuong, B.C.: Picture fuzzy sets. J. Comput. Sci. Cybern. 30(4), 419–430 (2014)

    Google Scholar 

  15. Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25(5), 1222–1230 (2016)

    Article  Google Scholar 

  16. Kutlu Gündoğdu, F., Kahraman, C.: Spherical fuzzy sets and spherical fuzzy TOPSIS method. J. Intell. Fuzzy Syst. 36(1), 337–352 (2019)

    Article  Google Scholar 

  17. Senapati, T., Yager, R.R.: Fermatean fuzzy sets. J. Ambient Intell. Human. Comput. 1–12 (2019)

    Google Scholar 

  18. Yildiz, N., Kahraman, C.: Evaluation of social sustainable development factors using Buckley’s fuzzy AHP based on Z-numbers. In International Conference on Intelligent and Fuzzy Systems, pp. 770–778. Springer, Cham, July 2019

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Industrial Engineering Department, Istanbul Technical University, Macka, Istanbul, Turkey

    Irem Ucal Sari & Cengiz Kahraman

Authors
  1. Irem Ucal Sari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cengiz Kahraman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irem Ucal Sari .

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

    Cengiz Kahraman

  2. Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

    Sezi Cevik Onar

  3. Department of Industrial Engineering, Istanbul Technical University, Ä°stanbul, Turkey

    Basar Oztaysi

  4. Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

    Irem Ucal Sari

  5. Industrial Engineering Department, Yildiz Technical University, Istanbul, Turkey

    Selcuk Cebi

  6. Industrial Engineering Department, Galatasaray University, Istanbul, Turkey

    A. Cagri Tolga

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sari, I.U., Kahraman, C. (2021). Intuitionistic Fuzzy Z-numbers. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I., Cebi, S., Tolga, A. (eds) Intelligent and Fuzzy Techniques: Smart and Innovative Solutions. INFUS 2020. Advances in Intelligent Systems and Computing, vol 1197. Springer, Cham. https://doi.org/10.1007/978-3-030-51156-2_154

Download citation

Publish with us

Policies and ethics

Search

Navigation