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An extended COPRAS method based on complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean aggregation operators

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Abstract

The complex q-rung orthopair fuzzy 2-tuple linguistic set (Cq-ROFTLS), which merges the concepts of complex q-rung orthopair fuzzy sets (Cq-ROFS) and 2-tuple linguistic terms, offers significant advantages in dealing with uncertain and imprecise information during decision-making by effectively representing two-dimensional information within a single set. Notably, the Cq-ROFTLS introduces phase terms that empower experts to express their perspectives flexibly, particularly enhancing its capacity to address periodic elements. To address uncertainty, this approach employs complex values to quantify both membership and non-membership degrees within 2-tuple linguistic environment. Additionally, this research introduces the generalized Maclaurin symmetric mean (MSM) aggregation operator, specifically designed for Cq-ROFTL information. This introduces the Cq-ROFTLMSM and its dual form, the Cq-ROFTL Dual MSM (Cq-ROFTLDMSM), each carrying valuable properties. In cases where the importance of input factors varies, the study proposes the Cq-ROFTL weighted MSM (Cq-ROFTLWMSM) and its dual form, the Cq-ROFTL weighted dual MSM (Cq-ROFTLWDMSM). These operators not only make their debut but also showcase their properties and applications. They flexibly adjust to the significance of inputs, leading to a more refined decision-making process. The methodology extends to address multi-attribute group decision-making (MAGDM) within the Cq-ROFTL framework using the Complex Proportional Assessment (COPRAS) method. The introduction of new aggregation techniques further enhances this approach. A practical illustration involving the selection of the optimal bio-energy production technology (BPT) highlights the real-world effectiveness of the methodology. Through thorough comparisons and a focused exploration of advantages, the study effectively validates the merits of this approach.

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References

  • Aherwar A, Pruncu CI, Mia M (2022) Optimal design based on fabricated SiC/B4C/porcelain filled aluminium alloy matrix composite using hybrid AHP/CRITIC-COPRAS approach. Silicon. 14(2):603–615

    Article  Google Scholar 

  • Ajay D, Aldring J, Jaganath T S (2022) Software selection for IT industry using complex \(q\)-rung orthopair fuzzy MCDM model. In International Conference on Intelligent and Fuzzy Systems, Springer, Cham, 641-648 https://doi.org/10.1007/978-3-031-09173-5-74

  • Akram M, Naz S, Feng F, Shafiq A (2023) Assessment of hydropower plants in Pakistan: Muirhead mean-based 2-tuple linguistic t-spherical fuzzy model combining SWARA with COPRAS. Arab J Sci Eng 48(5):5859–5888

    Article  Google Scholar 

  • Akram M, Naz S, Edalatpanah SA, Samreen S (2023) A hybrid decision-making framework under 2-tuple linguistic complex \(q\)-rung orthopair fuzzy Hamy mean aggregation operators. Comput Appl Math 42(3):118

    Article  MathSciNet  Google Scholar 

  • Akram M, Naz S, Feng F, Ali G, Shafiq A (2023) Extended MABAC method based on 2-tuple linguistic T-spherical fuzzy sets and Heronian mean operators: an application to alternative fuel selection. AIMS Math 8(5):10619–10653

    Article  MathSciNet  Google Scholar 

  • Akram M, Naz S, Abbas T (2023) Complex \(q\)-rung orthopair fuzzy 2-tuple linguistic group decision-making framework with Muirhead mean operators. Artificial Intell Rev 56:10227–10274

    Article  Google Scholar 

  • Ali Z, Mahmood T (2020) Maclaurin symmetric mean operators and their applications in the environment of complex \(q\)-rung orthopair fuzzy sets. Comput Appl Math 39(3):1–27

    Article  MathSciNet  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MathSciNet  Google Scholar 

  • Bathrinath S, Venkadesh S, Suprriyan SS, Koppiahraj K, Bhalaji RKA (2022) A fuzzy COPRAS approach for analysing the factors affecting sustainability in ship ports. Mater Today 50:1017–1021

    Google Scholar 

  • Cuiping Wei, Liao Huchang (2016) A multigranularity linguistic group decision-making method based on hesitant 2-tuple sets. Int J Intell Syst 31(6):612–634

    Article  Google Scholar 

  • Garg H, Ali Z, Mahmood T (2021) Algorithms for complex interval-valued \(q\)-rung orthopair fuzzy sets in decision making based on aggregation operators, AHP, and TOPSIS. Expert Syst 38(1):e12609. https://doi.org/10.1111/exsy.12609

    Article  Google Scholar 

  • Garg H, Naz S, Ziaa F, Shoukat Z (2021) A ranking method based on Muirhead mean operator for group decision making with complex interval-valued \(q\)-rung orthopair fuzzy numbers. Soft Comput 25(22):14001–14027

    Article  Google Scholar 

  • Herrera F, Martinez L (2000) An approach for combining linguistic and numerical information based on the 2-tuple fuzzy linguistic representation model in decision-making. Int J Uncertainty Fuzziness Know-Based Syst 8(05):539–562

    Article  MathSciNet  Google Scholar 

  • Huang L, Mao L X, Chen Y, Liu H C (2022) New method for emergency decision making with an integrated regret theory-EDAS method in 2-tuple spherical linguistic environment. Applied Intelligence. 1-14 https://doi.org/10.1007/s10489-021-02875-5

  • Kamaci H (2022) Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications. Complex Intell Syst 8(2):1281–1305

    Article  MathSciNet  Google Scholar 

  • Maclaurin C (1729) A second letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans R Soc Lond Ser A 1729(36):59–96

    Google Scholar 

  • Masoomi B, Sahebi IG, Fathi M, Yildirim F, Ghorbani S (2022) Strategic supplier selection for renewable energy supply chain under green capabilities (fuzzy BWM-WASPAS-COPRAS approach). Energy Strategy Rev 40:100815

    Article  Google Scholar 

  • Naz S, Akram M, Muzammal M (2023) Group decision-making based on 2-tuple linguistic T-spherical fuzzy COPRAS method. Soft Computi 27(6):2873–2902

    Article  Google Scholar 

  • Naz S, Akram M, Hassan MMU, Fatima A (2023) A hybrid DEMATEL-TOPSIS approach using 2-tuple linguistic \(q\)-rung orthopair fuzzy information and its application in renewable energy resource selection. Int J Inform Technol Decision Making. https://doi.org/10.1142/S0219622023500323

    Article  Google Scholar 

  • Naz S, Akram M, Davvaz B, Saadat A (2023b) A new decision-making framework for selecting the river crossing project under dual hesitant \(q\)-rung orthopair fuzzy 2-tuple linguistic environment. Soft Comput 27:12021–12047

    Article  Google Scholar 

  • Naz S, Akram M, Al-Shamiri M M A, Saeed M R(2022) Evaluation of network security service provider using 2-tuple linguistic complex-rung orthopair fuzzy COPRAS method. Complexity. 2022, https://doi.org/10.1155/2022/4523287

  • Naz S, Hassan M M, Fatima A, Martinez D J, Mendoza E O, Butt S A(2023) A decision-making mechanism for multi-attribute group decision-making using 2-tuple linguistic T-spherical fuzzy maximizing deviation method. Granular Computing. 1-29 https://doi.org/10.1007/s41066-023-00388-9

  • Ning B, Wei G, Lin R, Guo Y (2022) A novel MADM technique based on extended power generalized Maclaurin symmetric mean operators under probabilistic dual hesitant fuzzy setting and its application to sustainable suppliers selection. Expert Syst Appl 204:117419

    Article  Google Scholar 

  • Qin J, Liu X (2015) Approaches to uncertain linguistic multiple attribute decision making based on dual Maclaurin symmetric mean. J Intell Fuzzy Syst 29(1):171–186

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Wang H, Zhang F(2022) Complex Pythagorean uncertain linguistic group decision-making model based on Heronian mean aggregation operator considering uncertainty, interaction and interrelationship. Complex & Intelligent Systems. 1-30 https://doi.org/10.1007/s40747-022-00749-y

  • Xiong SH, Chen ZS, Chiclana F, Chin KS, Skibniewski MJ (2022) Proportional hesitant 2-tuple linguistic distance measurements and extended VIKOR method: Case study of evaluation and selection of green airport plans. Int J Intell Syst 37(7):4113–4162

    Article  Google Scholar 

  • Yager, R. R (2013) Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) (pp. 57-61). IEEE. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375

  • Yager RR (2016) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230

    Article  Google Scholar 

  • Yang Z, Garg H (2022) Interaction power partitioned Maclaurin Symmetric mean operators under \(q\)-rung orthopair uncertain linguistic information. Int J Fuzzy Syst 24(2):1079–1097

    Article  Google Scholar 

  • Yue D, You F, Snyder SW (2014) Biomass-to-bioenergy and biofuel supply chain optimization: overview, key issues and challenges. Comput Chem Eng 66:36–56

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inform Control 8(3):338–353

    Article  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inform Sci 8(3):199–249

    Article  MathSciNet  Google Scholar 

  • Zavadskas EK, Kaklauskas A, Sarka V (1994) The new method of multicriteria complex proportional assessment of projects. Technol Econ Dev Econ 1(3):131–139

    Google Scholar 

  • Zhang X (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31(6):593–611

    Article  Google Scholar 

  • Zhong Y, Cao L, Zhang H, Qin Y, Huang M, Luo X (2022) Hesitant fuzzy power Maclaurin symmetric mean operators in the framework of Dempster-Shafer theory for multiple criteria decision making. J Ambient Intell Human Comput 13(4):1777–1797

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan

    Sumera Naz

  2. School of Mathematics, Minhaj University, Lahore, Pakistan

    Rida Mehreen

  3. Department of Mathematics, Abbotabad University Science and Technology, Abbottabad, Pakistan

    Tahir Abbas

  4. Universidad de la Costa, Barranquilla, Colombia

    Gabriel Piñeres-Espitia

  5. School of Systems and Technology, Department of Computer Science, University of Management and Technology, Lahore, Pakistan

    Shariq Aziz Butt

Authors
  1. Sumera Naz
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  2. Rida Mehreen
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  3. Tahir Abbas
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  4. Gabriel Piñeres-Espitia
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  5. Shariq Aziz Butt
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Correspondence to Sumera Naz.

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Naz, S., Mehreen, R., Abbas, T. et al. An extended COPRAS method based on complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean aggregation operators. J Ambient Intell Human Comput 15, 2119–2142 (2024). https://doi.org/10.1007/s12652-023-04742-2

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