Skip to main content

Advertisement

Springer Nature Link
Log in

A Bipolar Complex Fuzzy CRITIC-ELECTRE III Approach Using Einstein Averaging Aggregation Operators for Enhancing Decision Making in Renewable Energy Investments

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

Abstract

Faced with rapidly rising energy demand in industrialised societies and widespread global concern, countries are actively promoting the transition from conventional to renewable energy systems. The goal is to invest in renewable energy in the most efficient way to meet rising energy demand and reduce the challenges posed by climate change. However, decision makers must carefully weigh various factors when selecting the most appropriate renewable energy investment projects. This paper presents a novel method for Multi-Attribute Decision Making(MADM) that uses the Bipolar Complex Fuzzy(BCF) to convey the vagueness and uncertainty of decision makers, so that the result obtained better reflects the actual scenario and the subjective biases of decision makers. We defined BCF Einstein Weighted Averaging (BCFEWA) operator and BCF Einstein Ordered Weighted Averaging (BCFEOWA) operator to aggregate evaluation information. Then we discussed some properties of the proposed aggregation operators. Additionally, we present an integrated MADM technique grounded in the BCF framework that combines the CRiteria Importance Through Intercriteria Correlation (CRITIC) and ELECTRE III methods. Specifically, the CRITIC method determines attribute weights, and the ELECTRE III method ranking the alternatives to determine the best renewable energy investment projects. After analysing the results and comparisons, it can be inferred that the suggested methodology offers an effective evaluation process.

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

Similar content being viewed by others

Explore related subjects

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

Data availability

All data used in this study are included in the article. Further inquiries can be directed to the corresponding author.

References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (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  MathSciNet  MATH  Google Scholar 

  3. Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decision. In: 2009 IEEE International Conference on Fuzzy Systems, pp. 1378–1382. IEEE, Jeju Island, South Korea (2009). https://doi.org/10.1109/FUZZY.2009.5276884

  4. Yager, R.R., Abbasov, A.M.: Pythagorean membership grades, complex numbers, and decision making: pythagorean membership grades and fuzzy subsets. Int. J. Intell. Syst. 28(5), 436–452 (2013). https://doi.org/10.1002/int.21584

    Article  MATH  Google Scholar 

  5. 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). https://doi.org/10.1016/j.engappai.2019.05.012

    Article  MATH  Google Scholar 

  6. Kutlu Gündoğdu, F.: Analyzing critical barriers of smart energy city in Turkey based on two-dimensional uncertainty by hesitant z-fuzzy linguistic terms. Eng. Appl. Artif. Intell. 113, 104935 (2022). https://doi.org/10.1016/j.engappai.2022.104935

    Article  MATH  Google Scholar 

  7. Yang, S., Pan, Y., Zeng, S.: Decision making framework based Fermatean fuzzy integrated weighted distance and TOPSIS for green low-carbon port evaluation. Eng. Appl. Artif. Intell. 114, 105048 (2022). https://doi.org/10.1016/j.engappai.2022.105048

    Article  MATH  Google Scholar 

  8. Ul Haq, R.S., Saeed, M., Mateen, N., Siddiqui, F., Naqvi, M., Yi, J.B., Ahmed, S.: Sustainable material selection with crisp and ambiguous data using single-valued neutrosophic-MEREC-MARCOS framework. Appl. Soft Comput. 128, 109546 (2022). https://doi.org/10.1016/j.asoc.2022.109546

    Article  Google Scholar 

  9. Pan, X., Wang, Y., He, S.: A new regret theory-based risk decision-making method for renewable energy investment under uncertain environment. Comput. Ind. Eng. 170, 108319 (2022). https://doi.org/10.1016/j.cie.2022.108319

    Article  MATH  Google Scholar 

  10. Mishra, A.R., Rani, P., Cavallaro, F., Mardani, A.: A similarity measure-based Pythagorean fuzzy additive ratio assessment approach and its application to multi-criteria sustainable biomass crop selection. Appl. Soft Comput. 125, 109201 (2022). https://doi.org/10.1016/j.asoc.2022.109201

    Article  MATH  Google Scholar 

  11. Rao, C., Gao, M., Goh, M., Xiao, X.: Green supplier selection mechanism based on information environment of Z-numbers. Cogn. Comput. 15, 520–533 (2023). https://doi.org/10.1007/s12559-022-10055-x

    Article  MATH  Google Scholar 

  12. Zhang, W.R.: Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. In: Proc. of IEEE conf., pp. 305–309 (1994). https://doi.org/10.1109/IJCF.1994.375115

  13. Alkouri, A.U.M.J., Massa’deh, M.O., Ali, M.: On bipolar complex fuzzy sets and its application. J. Intell. Fuzzy Syst. 39(1), 383–397 (2020). https://doi.org/10.3233/JIFS-191350

    Article  MATH  Google Scholar 

  14. Mahmood, T., Rehman, U.: A novel approach towards bipolar complex fuzzy sets and their applications in generalized similarity measures. Int. J. Intell. Syst. 37(1), 535–567 (2022). https://doi.org/10.1002/int.22639

    Article  MATH  Google Scholar 

  15. Roy, A., Saha, A., Chatterjee, P., Dutta, D., Rastogi, R., Kottapalli, R.: A consensus model with bipolar fuzzy archimedean-dombi operators for group decision-making. Soft Comput. (2023). https://doi.org/10.1007/s00500-023-08750-4

    Article  Google Scholar 

  16. Mahmood, T., Rehman, U.: A method to multi-attribute decision making technique based on Dombi aggregation operators under bipolar complex fuzzy information. Comput. Appl. Math. 41(1), 47 (2022). https://doi.org/10.1007/s40314-021-01735-9

    Article  MathSciNet  MATH  Google Scholar 

  17. Mahmood, T., Rehman, U.U., Naeem, M., Mahmood, T., Rehman, U.U., Naeem, M.: A novel approach towards Heronian mean operators in multiple attribute decision making under the environment of bipolar complex fuzzy information. AIMS Math. 8, 1848–1870 (2023). https://doi.org/10.3934/math.2023095

    Article  MathSciNet  MATH  Google Scholar 

  18. Mahmood, T., Ur Rehman, U., Ali, Z.: Analysis and application of Aczel-Alsina aggregation operators based on bipolar complex fuzzy information in multiple attribute decision making. Inf. Sci. 619, 817–833 (2023). https://doi.org/10.1016/j.ins.2022.11.067

    Article  MATH  Google Scholar 

  19. Mahmood, T., Rehman, U., Ahmmad, J., Santos-García, G.: Bipolar complex Fuzzy Hamacher aggregation operators and their applications in multi-attribute decision making. Mathematics 10(1), 23 (2021). https://doi.org/10.3390/math10010023

    Article  MATH  Google Scholar 

  20. Mesiar, R., Stupňanová, A., Jin, L.: Bipolar ordered weighted averages: BIOWA operators. Fuzzy Sets Syst. 433, 108–121 (2021). https://doi.org/10.1016/j.fss.2021.01.010

    Article  MathSciNet  MATH  Google Scholar 

  21. Rehman, U.U., Mahmood, T., Albaity, M., Hayat, K., Ali, Z.: Identification and prioritization of DevOps success factors using bipolar complex fuzzy setting with frank aggregation operators and analytical hierarchy process. IEEE Access 10, 74702–74721 (2022). https://doi.org/10.1109/ACCESS.2022.3190611

    Article  MATH  Google Scholar 

  22. Mahmood, T., Rehman, U., Ali, Z., Aslam, M.: Bonferroni mean operators based on bipolar complex fuzzy setting and their applications in multi-attribute decision making. AIMS Math. 7(9), 17166–17197 (2022). https://doi.org/10.3934/math.2022945

    Article  MathSciNet  MATH  Google Scholar 

  23. Mahmood, T., Rehman, U.U.: Digital technology implementation and impact of artificial intelligence based on bipolar complex fuzzy Schweizer-Sklar power aggregation operators. Appl. Soft Comput. 143, 110375 (2023). https://doi.org/10.1016/j.asoc.2023.110375

    Article  MATH  Google Scholar 

  24. Rehman, U., Mahmood, T.: The generalized dice similarity measures for bipolar complex fuzzy set and its applications to pattern recognition and medical diagnosis. Comput. Appl. Math. 41(6), 265 (2022). https://doi.org/10.1007/s40314-022-01948-6

    Article  MathSciNet  MATH  Google Scholar 

  25. Mahmood, T., Jaleel, A., Rehman, U.U.: Pattern recognition and medical diagnosis based on trigonometric similarity measures for bipolar complex fuzzy soft sets. Soft. Comput. 27(16), 11125–11154 (2023). https://doi.org/10.1007/s00500-023-08176-y

    Article  MATH  Google Scholar 

  26. Mardani, A., Hooker, R.E., Ozkul, S., Yifan, S., Nilashi, M., Sabzi, H.Z., Fei, G.C.: Application of decision making and fuzzy sets theory to evaluate the healthcare and medical problems: a review of three decades of research with recent developments. Expert Syst. Appl. 137, 202–231 (2019). https://doi.org/10.1016/j.eswa.2019.07.002

    Article  Google Scholar 

  27. Deveci, M., Gokasar, I., Mishra, A.R., Rani, P., Ye, Z.: Evaluation of climate change-resilient transportation alternatives using fuzzy Hamacher aggregation operators based group decision-making model. Eng. Appl. Artif. Intell. (2023). https://doi.org/10.1016/j.engappai.2023.105824

    Article  MATH  Google Scholar 

  28. Al-Quran, A., Jamil, N., Tehrim, S.T., Riaz, M., Al-Quran, A., Jamil, N., Tehrim, S.T., Riaz, M.: Cubic bipolar fuzzy VIKOR and ELECTRE-II algorithms for efficient freight transportation in industry 4.0. AIMS Math. 8, 24484–24514 (2023). https://doi.org/10.3934/math.20231249

    Article  MATH  Google Scholar 

  29. Jana, C., Garg, H., Pal, M., Sarkar, B., Wei, G.: MABAC framework for logarithmic bipolar fuzzy multiple attribute group decision-making for supplier selection. Complex Intell. Syst. (2023). https://doi.org/10.1007/s40747-023-01108-1

    Article  MATH  Google Scholar 

  30. Liu, P., Shen, M., Pedrycz, W.: MAGDM framework based on double hierarchy bipolar hesitant fuzzy linguistic information and its application to optimal selection of talents. Int. J. Fuzzy Syst. 24(4), 1757–1779 (2022). https://doi.org/10.1007/s40815-021-01231-6

    Article  MATH  Google Scholar 

  31. Sharma, J., Tyagi, M., Bhardwaj, A.: Mathematical depiction of costing perspectives allied with the dynamics of processed food supply chain. J. Enterp. Inf. Manag. (2023). https://doi.org/10.1108/JEIM-02-2022-0057

    Article  MATH  Google Scholar 

  32. Garai, T., Garg, H., Biswas, G.: A fraction ranking-based multi-criteria decision-making method for water resource management under bipolar neutrosophic fuzzy environment. Artif. Intell. Rev. (2023). https://doi.org/10.1007/s10462-023-10514-3

    Article  MATH  Google Scholar 

  33. Garai, T., Garg, H., Biswas, G.: Possibilistic index-based multi-criteria decision-making with an unknown weight of air pollution model under bipolar fuzzy environment. Soft. Comput. 27, 17991–18009 (2023). https://doi.org/10.1007/s00500-023-09008-9

    Article  MATH  Google Scholar 

  34. Zhao, M., Wei, G., Guo, Y., Chen, X.: CPT-TODIM method for interval-valued bipolar fuzzy multiple attribute group decision making and application to industrial control security service provider. Technol. Econ. Dev. Econ. 27(5), 1186–1206 (2021). https://doi.org/10.3846/tede.2021.15044

    Article  MATH  Google Scholar 

  35. Riaz, M., Habib, A., Saqlain, M., Yang, M.-S.: Cubic bipolar fuzzy-VIKOR method using new distance and entropy measures and einstein averaging aggregation operators with application to renewable energy. Int. J. Fuzzy Syst. 25, 510–543 (2022). https://doi.org/10.1007/s40815-022-01383-z

    Article  Google Scholar 

  36. Garai, T., Garg, H.: Multi-criteria decision making of water resource management problem (in Agriculture field, Purulia district) based on possibility measures under generalized single valued non-linear bipolar neutrosophic environment. Expert Syst. Appl. 205, 117715 (2022). https://doi.org/10.1016/j.eswa.2022.117715

    Article  Google Scholar 

  37. Baidya, J., Garg, H., Saha, A., Mishra, A.R., Rani, P., Dutta, D.: Selection of third party reverses logistic providers: An approach of BCF-CRITIC-MULTIMOORA using Archimedean power aggregation operators. Complex Intell. Syst. 7(5), 2503–2530 (2021). https://doi.org/10.1007/s40747-021-00413-x

    Article  Google Scholar 

  38. Kamacı, H., Garg, H., Petchimuthu, S.: Bipolar trapezoidal neutrosophic sets and their Dombi operators with applications in multicriteria decision making. Soft. Comput. 25(13), 8417–8440 (2021). https://doi.org/10.1007/s00500-021-05768-4

    Article  MATH  Google Scholar 

  39. Mahmood, T., Rehman, U.: Multi-attribute decision-making method based on bipolar complex fuzzy Maclaurin symmetric mean operators. Comput. Appl. Math. 41(7), 331 (2022). https://doi.org/10.1007/s40314-022-02016-9

    Article  MathSciNet  MATH  Google Scholar 

  40. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners, vol. 221. Springer, Berlin, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73721-6

    Book  MATH  Google Scholar 

  41. Mahmood, T., Rehman, U.U.: Providing decision-making approaches for the assessment and selection of cloud computing using bipolar complex fuzzy Einstein power aggregation operators. Eng. Appl. Artif. Intell. 129, 107650 (2024). https://doi.org/10.1016/j.engappai.2023.107650

    Article  MATH  Google Scholar 

  42. Diakoulaki, D.: Determining objective weights in multiple criteria problems: the critic method. Comput. Oper. Res. 22(7), 763–770 (1995). https://doi.org/10.1016/0305-0548(94)00059-H

    Article  MATH  Google Scholar 

  43. Roy, B.: Algorithme de classement basé sur une représentation des préférence en présence de criteres multiples. Cahiers du CERO 20, 3–24 (1978)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Economics and Management, Shanxi University, Taiyuan, 030006, Shanxi, China

    Jianping Fan, Ge Hao & Meiqin Wu

Authors
  1. Jianping Fan
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Ge Hao
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Meiqin Wu
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Meiqin Wu.

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

Fan, J., Hao, G. & Wu, M. A Bipolar Complex Fuzzy CRITIC-ELECTRE III Approach Using Einstein Averaging Aggregation Operators for Enhancing Decision Making in Renewable Energy Investments. Int. J. Fuzzy Syst. 26, 2359–2369 (2024). https://doi.org/10.1007/s40815-024-01739-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-024-01739-7

Keywords