Skip to main content
SpringerLink
Log in

Score Function-Based Effective Ranking of Interval-Valued Fermatean Fuzzy Sets and Its Applications to Multi-criteria Decision Making Problem

  • Chapter
  • First Online:
Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 420))

Abstract

Fermatean fuzzy sets (FFSs), an orthopair fuzzy set proposed by Senapati and Yager (Journal of Ambient Intelligence and Humanized Computing 11:663–674, 2020, [24]), can handle the situation with ambiguous and incomplete information in a more effective manner than the Pythagorean fuzzy sets presented by Yager (Pythagorean fuzzy subsets, 2013 Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp 57–61, 2013, [2]) and the intuitionistic fuzzy sets presented by Atanassov (Fuzzy Sets and Systems 20:87–96, 1986, [3]). Sergi et al. (Journal of Intelligent & Fuzzy Systems 42:365–376, 2022, [40]) initiated interval-valued Fermatean fuzzy sets (IVFFSs) and established IVFFS ordering, as well as some mathematical operations. In addition, Jeevraj (Expert Systems with Applications 185:1–20, 2021, [37]) introduced the concept of a score and accuracy function for IVFFSs. The main objective of this chapter is to suggest some score functions for acceptable ranking of IVFFSs, as well as the interval-valued Fermatean fuzzy TOPSIS method for solving multi-criteria decision making problems. Here, we have proposed six new variants of score functions for effective ranking of interval-valued Fermatean fuzzy sets. Depending on various types of score functions, we have used a TOPSIS-based multi-criteria decision making (MCDM) problem in which decision makers’ (DMs’) preference knowledge is summarized in the pattern of interval-valued Fermatean fuzzy sets. To illustrate the usefulness of the proposed method, a computational paradigm has been considered. Finally, concluding remarks and future scope of research have been mentioned.

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 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
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, 338–353 (1965)

    Article  MATH  Google Scholar 

  2. Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manage. Sci. 17, 141–164 (1970)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Fei, L., Wang, H., Chen, L., Deng, Y.: A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators. Iran. J. Fuzzy Syst. 15(5), 31–49 (2018)

    MathSciNet  Google Scholar 

  5. Zhang, R., Ashuri, B., Deng, Y.: A novel method for forecasting time series based on fuzzy logic and visibility graph. Adv. Data Anal. Classif. 11(4), 759–783 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gorzalczany, M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 21(1), 1–17 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  7. Turksen, I.B.: Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 20(2), 191–210 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Atanassov, K.T., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 1–17 (1987)

    MathSciNet  MATH  Google Scholar 

  9. Atanassov, K.T.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)

    Book  MATH  Google Scholar 

  10. Atanassov, K.T., Vassilev, P.M., Tsvetkov, R.T.: Intuitionistic Fuzzy Sets, Measures and Integrals. Professor Marin Drinov Academic Publishing House, Sofia (2013)

    Google Scholar 

  11. Atanassov, K.T.: A Second type of Intuitionistic fuzzy sets. BUSE-FAL 56, 66–70 (1983)

    Google Scholar 

  12. Atanassov, K.T.: Geometric interpretation of the elements of the intuitionistic fuzzy objects. Int. J. Bioautom. 20(S1), S27–S42 (2016)

    Google Scholar 

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

    Google Scholar 

  14. Yager, R.R.: Pythagorean membership grades in multi-criteria decision making. IEEE Trans. Fuzzy Syst. 22, 958–965 (2014)

    Article  Google Scholar 

  15. Garg, H.: A linear programming method based on an improved score function for interval valued Pythagorean fuzzy numbers and its application to decision-making. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 26, 67–80 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  16. Garg, H.: A new improved score function of an interval valued Pythagorean fuzzy set based TOPSIS method. Int. J. Uncertainty Quant. 7, 463–474 (2017)

    Article  Google Scholar 

  17. Zhang, X., Xu, Z.: Extention of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int. J. Intell. Syst. 29, 1061–1078 (2014)

    Article  Google Scholar 

  18. Zhang, X.: A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int. J. Intell. Syst. 31, 593–611 (2016)

    Article  Google Scholar 

  19. Gou, X., Xu, Z., Liao, H.: Alternative queuing method for multiple criteria decision making with hybrid fuzzy and ranking information. Inf. Sci. 357, 144–160 (2016)

    Article  Google Scholar 

  20. Geng, Y., Liu, P., Teng, F., Liu, Z.: Pythagorean fuzzy uncertain linguistic TODIM method and their application to multiple criteria group decision making. Int. J. Intell. Syst. 33, 3383–3395 (2017)

    Google Scholar 

  21. Jing, N., Xian, S., Xiao, Y.: Pythagorean triangular fuzzy linguistic bonferroni mean operators and their application for multi-attribute decision making, In: 2nd IEEE International Conference on Computational Intelligence and Applications (ICCIA), pp. 435–439 (2017)

    Google Scholar 

  22. Senapati, T., Yager, R.R.: Fermatean fuzzy sets. J. Ambient Intell. Humaniz. Comput. 11, 663–674 (2020)

    Article  Google Scholar 

  23. Senapati, T., Yager, R.R.: Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Eng. Appl. Artif. Intell. 85, 112–121 (2019)

    Article  Google Scholar 

  24. Li, Z., Wei, G., Lu, M.: Pythagorean fuzzy hamy mean operators in multiple attribute group decision making and their application to supplier selection. Symmetry 10, 505 (2018)

    Article  Google Scholar 

  25. Zhou, J., Su, W., Balezentis, T., Streimikiene, D.: Multiple criteria group decision making considering symmetry with regards to the positive and negative ideal solution via the Pythagorean normal cloud model for application to economic decision. Symmetry 10(5), 140 (2018)

    Article  Google Scholar 

  26. Boltruk, E.: Pythagorean fuzzy CODAS and its application to supplier selection in a manufacturing firm. J. Enterp. Inf. Manag. 31, 550–564 (2018)

    Article  Google Scholar 

  27. Qin, J.: Generalized Pythagorean fuzzy Maclaurin symmetric means and its application to multiple attribute SIR group decision model. Int. J. Fuzzy Syst. 20, 943–957 (2018)

    Article  MathSciNet  Google Scholar 

  28. Wan, S.-P., Li, S.-Q., Dong, J.-Y.: A three phase method for Pythagorean fuzzy multi attribute group decision making and application to haze management. Comput. Ind. Eng. 123, 348–363 (2018)

    Article  Google Scholar 

  29. Lin, Y.-L., Ho, L.-H., Yeh, S.-L., Chen, T.-Y.: A Pythagorean fuzzy topsis method based on novel correlation measures and its application to multiple criteria decision analysis of inpatient stoke rehabilitiation. Int. J. Comput. Intell. Syst. 12(1), 410–425 (2018)

    Article  Google Scholar 

  30. Chen, T.-Y.: An outranking approach using a risk attitudinal assignment model involving Pythagorean fuzzy information and its application to financial decision making. Appl. Soft. Comput. 71, 460–487 (2018)

    Article  Google Scholar 

  31. Sahoo, L.: Some score functions on Fermatean fuzzy sets and its application to bride selection based on TOPSIS method. Int. J. Fuzzy Syst. Appl. 10(3), 18–29 (2021)

    MathSciNet  Google Scholar 

  32. Sahoo, L.: A new score function based Fermatean fuzzy transportation problem. Results Control Opt. 4, 100040 (2021)

    Article  Google Scholar 

  33. Sahoo, L.: Similarity measures for Fermatean fuzzy sets and its applications in group decision-making. Decis. Sci. Lett. 11, 167–180 (2022)

    Article  Google Scholar 

  34. Senapati, T., Yager, R.R.: Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making. Informatica 30(2), 391–412 (2019)

    Article  MATH  Google Scholar 

  35. Senapati, T., Chen, G.: Some novel interval-valued Pythagorean fuzzy aggregation operator based on Hamacher triangular norms and their application in MADM issues. Comput. Appl. Math. 40(4), 1–27 (2021). https://doi.org/10.1007/s40314-021-01502-w

    Article  MathSciNet  MATH  Google Scholar 

  36. Jana, C., Senapati, T., Pal, M.: Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. Int. J. Intell. Syst. 34(9), 2019–2038 (2019)

    Article  Google Scholar 

  37. Jeevaraj, S.: Ordering of interval-valued Fermatean fuzzy sets and its applications. Expert Syst. Appl. 185, 1–20 (2021)

    Google Scholar 

  38. Bai, Z.-Y.: An interval valued intuitionistic fuzzy TOPSIS method based on an improved score function. Sci. World J. 2013, 1–6 (2013)

    Google Scholar 

  39. Ye, J.: Multicriteria fuzzy-decision making method based on a novel accuracy function under interval valued intuitionistic fuzzy environment. Expert Syst. Appl. 36(3), 6899–6902 (2009)

    Article  Google Scholar 

  40. Sergi, D., Sari, I.U., Senapati, T.: Extension of capital budgeting techniques using interval-valued Fermatean fuzzy sets. J. Intell. Fuzzy Syst. 42(1), 365–376 (2022)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer and Information Science, Raiganj University, Raiganj, 733134, India

    Laxminarayan Sahoo

  2. Department of Mathematics, Narajole Raj College, Paschim Medinipur, West Bengal, 721211, India

    Akul Rana

  3. School of Mathematics and Statistics, Southwest University, Beibei, Chongqing, 400715, China

    Tapan Senapati

  4. Machine Intelligence Institute, Iona College, New Rochelle, NY, 10801, USA

    Ronald R. Yager

Authors
  1. Laxminarayan Sahoo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akul Rana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tapan Senapati
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ronald R. Yager
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laxminarayan Sahoo .

Editor information

Editors and Affiliations

  1. Department of Computer and Information Science, Raiganj University, Raiganj, West Bengal, India

    Laxminarayan Sahoo

  2. School of Mathematics and Statistics, Southwest University, Chongqing, China

    Tapan Senapati

  3. Iona College, Machine Intelligence Institute, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sahoo, L., Rana, A., Senapati, T., Yager, R.R. (2023). Score Function-Based Effective Ranking of Interval-Valued Fermatean Fuzzy Sets and Its Applications to Multi-criteria Decision Making Problem. In: Sahoo, L., Senapati, T., Yager, R.R. (eds) Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain. Studies in Fuzziness and Soft Computing, vol 420. Springer, Singapore. https://doi.org/10.1007/978-981-19-4929-6_20

Download citation

Publish with us

Policies and ethics

Search

Navigation