Skip to main content

Advertisement

Springer Nature Link
Log in

Power Dombi Aggregation Operators for Complex Pythagorean Fuzzy Sets and Their Applications in Green Supply Chain Management

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Green supply chain management concerns the incorporation of globally sustainable methods into supply chain management techniques. The major goal is to decrease the environmental impact of the entire supply chain to increase the social, ecological, and economic relationships with other countries for business. In this manuscript, we aim to compute the Dombi operational laws based on the complex Pythagorean fuzzy (CPF) information. Furthermore, we construct the Dombi aggregation operators under the consideration of the CPF information, such as the CPF power Dombi averaging (CPFPDA) operator, CPF power weighted Dombi averaging (CPFPWDA) operator, CPF power Dombi geometric (CPFPDG) operator, and CPF power weighted Dombi geometric (CPFPWDG) operator. Some flexible properties for the invented operators are also discussed. Additionally, we develop the multi-attribute decision-making (MADM) method to evaluate the problem of green supply chain management based on the invented operators for CPF information. Finally, we use some numerical examples to show the supremacy and validity of the developed techniques by comparing their ranking results with the obtaining ranking results of the existing techniques.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

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

    Article  MATH  Google Scholar 

  2. Yager, R.R.: Aggregation operators and fuzzy systems modeling. Fuzzy Sets Syst. 67(2), 129–145 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wang, W.J.: New similarity measures on fuzzy sets and on elements. Fuzzy Sets Syst. 85(3), 305–309 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mahmood, T., Ali, Z.: Fuzzy superior mandelbrot sets. Soft. Comput. 26(18), 9011–9020 (2022)

    Article  MATH  Google Scholar 

  5. Sun, C.C.: A performance evaluation model by integrating fuzzy AHP and fuzzy TOPSIS methods. Expert Syst. Appl. 37(12), 7745–7754 (2010)

    Article  MATH  Google Scholar 

  6. Atanassov, K.: Intuitionistic fuzzy sets. In: VII ITKR’s Session (Deposed in Central Sci.—Techn. Library Bulg. Acad. Sci., 1697/84; Sofia, Bulgaria) (In Bulgarian) (1983)

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

    Article  MathSciNet  MATH  Google Scholar 

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

  9. Ali, Z., Mahmood, T., Ullah, K., Khan, Q.: Einstein geometric aggregation operators using a novel complex interval-valued Pythagorean fuzzy setting with application in green supplier chain management. Rep. Mech. Eng. 2(1), 105–134 (2021)

    Article  MATH  Google Scholar 

  10. Garg, H., Ali, Z., Mahmood, T., Ali, M.R., Alburaikan, A.: Schweizer-Sklar prioritized aggregation operators for intuitionistic fuzzy information and their application in multi-attribute decision-making. Alex. Eng. J. 67, 229–240 (2023)

    Article  MATH  Google Scholar 

  11. Mahmood, T., Ali, Z., Baupradist, S., Chinram, R.: TOPSIS method based on Hamacher Choquet-integral aggregation operators for Atanassov-Intuitionistic fuzzy sets and their applications in decision-making. Axioms 11(12), 715 (2022)

    Article  MATH  Google Scholar 

  12. Mahmood, T., Ahmmad, J., Ali, Z., Yang, M.S.: Confidence level aggregation operators based on intuitionistic fuzzy rough sets with application in medical diagnosis. IEEE Access 11, 8674–8688 (2023)

    Article  MATH  Google Scholar 

  13. Albaity, M., Mahmood, T., Ali, Z.: Impact of machine learning and artificial intelligence in business based on intuitionistic fuzzy soft WASPAS method. Mathematics 11(6), 1453 (2023)

    Article  MATH  Google Scholar 

  14. Ejegwa, P.A., Ahemen, S.: Enhanced intuitionistic fuzzy similarity operators with applications in emergency management and pattern recognition. Granul. Comput. 8(2), 361–372 (2023)

    Article  MATH  Google Scholar 

  15. Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)

    Article  MATH  Google Scholar 

  16. Bi, L., Dai, S., Hu, B., Li, S.: Complex fuzzy arithmetic aggregation operators. J. Intell. Fuzzy Syst. 36(3), 2765–2771 (2019)

    Article  MATH  Google Scholar 

  17. Bi, L., Dai, S., Hu, B.: Complex fuzzy geometric aggregation operators. Symmetry 10(7), 251 (2018)

    Article  MATH  Google Scholar 

  18. Liu, P., Ali, Z., Mahmood, T.: The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making. J. Intell. Fuzzy Syst. 39(3), 3351–3374 (2020)

    Article  MATH  Google Scholar 

  19. Mahmood, T., Ali, Z., Garg, H., Zedam, L., Chinram, R.: Correlation coefficient and entropy measures based on complex dual type-2 hesitant fuzzy sets and their applications. J. Math. 2021, 1–34 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  20. Alkouri, A.M.D.J.S., Salleh, A.R.: Complex intuitionistic fuzzy sets. In: AIP Conference Proceedings, vol. 1482, pp. 464–470. American Institute of Physics (2012)

  21. Ullah, K., Mahmood, T., Ali, Z., Jan, N.: On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell. Syst. 6, 15–27 (2020)

    Article  MATH  Google Scholar 

  22. Zhang, R., Wang, J., Zhu, X., Xia, M., Yu, M.: Some generalized Pythagorean fuzzy Bonferroni mean aggregation operators with their application to multiattribute group decision-making. Complexity 2017(6), 1–16 (2017). https://doi.org/10.1155/2017/5937376

    Article  MATH  Google Scholar 

  23. Garg, H.: Novel neutrality operation–based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis. Int. J. Intell. Syst. 34(10), 2459–2489 (2019)

    Article  MATH  Google Scholar 

  24. Garg, H.: New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int. J. Intell. Syst. 34(1), 82–106 (2019)

    Article  MATH  Google Scholar 

  25. Akram, M., Khan, A., Borumand Saeid, A.: Complex Pythagorean Dombi fuzzy operators using aggregation operators and their decision-making. Expert. Syst. 38(2), e12626 (2021)

    Article  MATH  Google Scholar 

  26. Akram, M., Peng, X., Al-Kenani, A.N., Sattar, A.: Prioritized weighted aggregation operators under complex Pythagorean fuzzy information. J. Intell. Fuzzy Syst. 39(3), 4763–4783 (2020)

    Article  MATH  Google Scholar 

  27. Akram, M., Peng, X., Sattar, A.: Multi-criteria decision-making model using complex Pythagorean fuzzy Yager aggregation operators. Arab. J. Sci. Eng. 46, 1691–1717 (2021)

    Article  MATH  Google Scholar 

  28. Jin, H., Hussain, A., Ullah, K., Javed, A.: Novel complex Pythagorean fuzzy sets under Aczel-Alsina operators and their application in multi-attribute decision making. Symmetry 15(1), 68 (2022)

    Article  MATH  Google Scholar 

  29. Aldring, J., Ajay, D.: Multicriteria group decision making based on projection measures on complex Pythagorean fuzzy sets. Granul. Comput. 8(1), 137–155 (2023)

    Article  Google Scholar 

  30. Yager, R.R.: The power average operator. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 31(6), 724–731 (2001)

    Article  MATH  Google Scholar 

  31. Xu, Z., Yager, R.R.: Power-geometric operators and their use in group decision making. IEEE Trans. Fuzzy Syst. 18(1), 94–105 (2009)

    MATH  Google Scholar 

  32. Dombi, J.: A general class of fuzzy operators, the DeMorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst. 8(2), 149–163 (1982)

    Article  MATH  Google Scholar 

  33. Xu, Z.: Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl. Based Syst. 24(6), 749–760 (2011)

    Article  MATH  Google Scholar 

  34. Wei, G., Lu, M.: Pythagorean fuzzy power aggregation operators in multiple attribute decision making. Int. J. Intell. Syst. 33(1), 169–186 (2018)

    Article  MATH  Google Scholar 

  35. Rani, D., Garg, H.: Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making. Expert. Syst. 35(6), e12325 (2018)

    Article  MATH  Google Scholar 

  36. Mahmood, T., Ali, Z.: Multi-attribute decision-making methods based on Aczel-Alsina power aggregation operators for managing complex intuitionistic fuzzy sets. Comput. Appl. Math. 42(2), 87 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  37. Hashemkhani Zolfani, S., Görçün, Ö.F., Küçükönder, H.: Evaluation of the special warehouse handling equipment (Turret Trucks) using integrated FUCOM and WASPAS techniques based on intuitionistic fuzzy Dombi aggregation operators. Arab. J. Sci. Eng. 48, 1–35 (2023)

    Article  Google Scholar 

  38. Khan, A.A., Ashraf, S., Abdullah, S., Qiyas, M., Luo, J., Khan, S.U.: Pythagorean fuzzy Dombi aggregation operators and their application in decision support system. Symmetry 11(3), 383 (2019)

    Article  MATH  Google Scholar 

  39. Garg, H., Olgun, M., Ünver, M., Türkarslan, E.: An extension of CODAS method for multi-criteria group decision making with complex intuitionistic fuzzy information via Dombi sine weighted arithmetic aggregation operators. Granul. Comput. 8, 1–14 (2023)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Business Administration, Shandong Women’s University, Jinan, 250300, Shandong, China

    Peide Liu

  2. Department of Mathematics and Statistics, Riphah International University, Islamabad, 44000, Pakistan

    Zeeshan Ali

  3. Technology Innovation Department, Inspur Cloud Information Technology Co., Ltd, Jinan, 250101, China

    Jianhua Ding

  4. Shandong Key Laboratory of New Smart Media, Jinan, 250014, Shandong, China

    Peide Liu

Authors
  1. Peide Liu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zeeshan Ali
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Jianhua Ding
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding authors

Correspondence to Peide Liu or Zeeshan Ali.

Ethics declarations

Conflict of interest

The authors have no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, P., Ali, Z. & Ding, J. Power Dombi Aggregation Operators for Complex Pythagorean Fuzzy Sets and Their Applications in Green Supply Chain Management. Int. J. Fuzzy Syst. 26, 1618–1633 (2024). https://doi.org/10.1007/s40815-024-01691-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-024-01691-6

Keywords