Skip to main content
SpringerLink
Log in

Decision Making Under Uncertainty via Generalized Parabolic Intuitionistic Fuzzy Numbers

  • Conference paper
  • First Online:
Recent Advances in Intelligent Information Systems and Applied Mathematics (ICITAM 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 863))

Abstract

In this paper, generalized parabolic intuitionistic fuzzy number has been studied. The aim of this paper is to present arithmetic operations of generalized parabolic intuitionistic fuzzy numbers by using \((\alpha , \beta )-\)cut method. In spite of these, exponential, logarithmic and \(n^{th}\) root of generalized parabolic intuitionistic fuzzy numbers have been done followed by numerical examples. Furthermore, rank of generalized parabolic intuitionistic fuzzy numbers has been evaluated based on mean and value. Finally, a decision making problem has been discussed to show its existence and applicability in real life.

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
Hardcover Book
USD 219.99
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

Institutional subscriptions

References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–356 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X

    Article  MATH  Google Scholar 

  2. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986). https://doi.org/10.1016/S0165-0114(86)80034-3

    Article  MATH  Google Scholar 

  3. Atanassov, K., Pasi, G., Yager, R.: Intuitionistic fuzzy interpretations of multi-person multi-criteria decision making. In: First International IEEE Symposium Intelligent Systems, pp. 859–868 (September 2002). https://doi.org/10.1080/00207720500382365

    Article  MathSciNet  Google Scholar 

  4. Li, D.F.: Multiattribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 70(1), 73–85 (2005)

    Article  MathSciNet  Google Scholar 

  5. Liu, H.W., Wang, G.: Multi-criteria decision-making methods based on intuitionistic fuzzy sets. Eur. J. Oper. Res. 179, 220–233 (2007)

    Article  Google Scholar 

  6. Li, D.F., Nan, J.X., Zhang, M.J.: A ranking method of triangular intuitionistic fuzzy numbers and application to decision making. Int. J. Comput. Intell. Syst. 3(5), 522–530 (2010)

    Article  Google Scholar 

  7. Shaw, A.K., Roy, T.K.: Some arithmetic operations on triangular intuitionistic fuzzy number and its application on reliability evaluation. Int. J. Fuzzy Math. Syst. 2(4), 363–382 (2012)

    Google Scholar 

  8. Shaw, A.K., Roy, T.K.: Trapezoidal intuitionistic fuzzy number with some arithmetic operations and its application on reliability evaluation. Int. J. Math. Oper. Res. 5(1), 55–73 (2013)

    Article  MathSciNet  Google Scholar 

  9. Ban, A.I., Tuse, D.A.: Trapezoidal/triangular intuitionistic fuzzy numbers versus interval-valued trapezoidal/triangular fuzzy numbers and applications to multicriteria decision making methods. Notes Intuitionistic Fuzzy Sets 20(2), 43–51 (2014)

    MATH  Google Scholar 

  10. Zeng, X.T., Li, D.F., Yu, G.F.: A value and ambiguity-based ranking method of trapezoidal intuitionistic fuzzy numbers and application to decision making. Sci. World J. 2014, 8 (2014). https://doi.org/10.1155/2014/560582

    Article  Google Scholar 

  11. Chen, S., Mu, Z., Zeng, S.: Atanassov’s intuitionistic fuzzy decision making with probabilistic information and distance measure. J. Intell. Fuzzy Syst. 28(1), 317–325 (2015)

    Article  MathSciNet  Google Scholar 

  12. Garg, H., Rani, D.: Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. Arab. J. Sci. Eng. 44(3), 1–20 (2018)

    Google Scholar 

  13. Jose, S.: Intuitionistic fuzzy approach to multi person decision making. Adv. Fuzzy Math. (AFM) 13(1), 9–14 (2018)

    MathSciNet  Google Scholar 

  14. Joshi, D., Kumar, S.: Improved accuracy function for interval-valued intuitionistic fuzzy sets and its application to multi-attributes group decision making. Cybern. Syst. 49(1), 64–76 (2018). https://doi.org/10.1080/01969722.2017.1412890

    Article  MathSciNet  Google Scholar 

  15. Fan, C.L., Song, Y., Fu, Q., Lei, L., Wang, X.: New operators for aggregating intuitionistic fuzzy information with their application in decision making. IEEE Access 6, 27214–27238 (2018)

    Article  Google Scholar 

  16. Dutta, P., Boruah, H., Ali, T.: Fuzzy arithmetic with and without using \(\alpha \)-cut method: a comparative study. Int. J. Latest Trends Comput. 2(1), 99–107 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dibrugarh University, Dibrugarh, 786004, India

    Palash Dutta, Bornali Saikia & Dhanesh Doley

Authors
  1. Palash Dutta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bornali Saikia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dhanesh Doley
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Palash Dutta .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

  2. Haldia Institute of Technology, Haldia, West Bengal, India

    Dipak Kumar Jana

  3. Maulana Abul Kalam Azad University of Technology, Haringhata, India

    Debasis Giri

  4. Haldia Institute of Technology, Haldia, India

    Arif Ahmed

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dutta, P., Saikia, B., Doley, D. (2020). Decision Making Under Uncertainty via Generalized Parabolic Intuitionistic Fuzzy Numbers. In: Castillo, O., Jana, D., Giri, D., Ahmed, A. (eds) Recent Advances in Intelligent Information Systems and Applied Mathematics. ICITAM 2019. Studies in Computational Intelligence, vol 863. Springer, Cham. https://doi.org/10.1007/978-3-030-34152-7_18

Download citation

Publish with us

Policies and ethics

Search

Navigation