Skip to main content
Springer Nature Link
Log in

2-tuple linguistic hesitant Pythagorean fuzzy MULTIMOORA with MSA and its application in the site selection problem of shared vehicle charging pile

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

The hesitant Pythagorean fuzzy set (HPFS) is a tool for making decisions in the face of ambiguity. The concept of 2-tuple linguistic hesitant Pythagorean fuzzy sets (2TLHPSs) is proposed on the condition that uncertain information may not be adequately represented in the hesitant Pythagorean fuzzy environment. First, in this work, it is proposed that the concept of 2TLHPSs, which is based on hesitant 2-tuple linguistic variables and Pythagorean fuzzy variables, introduced the operational laws and the comparison rules of 2TLHPSs. Second, based on the classical multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method, we propose a meta-synthesis approach (MSA) in the ranking aggregation method to consider the preference of decision points for three secondary rankings to avoid circular reasoning. This method used in the context of 2TLHPFS considers the weight in the model, and the parameter \(\varpi \) is quoted to reflect the preference of the decision-maker (DM) which improves the classical MULTIMOORA method. Finally, the practicability and reliability of our new method are explained and compared with other methods to reflect its flexibility by taking the location of the shared vehicle charging pile as an example.

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

Similar content being viewed by others

References

  • Altuntas S, Dereli T, Yilmaz MK (2015) Evaluation of excavator technologies: application of data fusion based multimoora methods. J Civ Eng Manag 21(8):977–997

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Beg I, Rashid T (2015) Hesitant 2-tuple linguistic information in multiple attributes group decision making. J Intell Fuzzy Syst 30(1):109–116

    Article  Google Scholar 

  • Brauers WK, Kazimieras ZE (2006) The MOORA method and its application to privatization in a transition economy. Control Cybern 35(2):445–469

    MathSciNet  MATH  Google Scholar 

  • Brauers WK, Zavadskas EK (2012) Robustness of MULTIMOORA: a method for multi-objective optimization. Informatica (Lith Acad Sci) 23(1):1–25

    MathSciNet  MATH  Google Scholar 

  • Brauers WK, Zavadskas E, Kazimieras (2010) Project management by multimoora as an instrument for transition economies. Technol Econ Dev Econ 16(1):5–24

    Article  Google Scholar 

  • Chen L, Xu HY, Ke GY (2021) A PROMETHEE II approach based on probabilistic hesitant fuzzy linguistic information with applications to multi-criteria group decision-making (ICSSE 2020). Int J Fuzzy Syst 23:1556–1580

    Article  Google Scholar 

  • Delgosha MS, Hajiheydari N (2020) Extended intuitionistic fuzzy VIKOR method in group decision making: the case of vendor selection decision. Int J Soc Sci Bus 14(5):351–358

    Google Scholar 

  • Deng XM, Wei GW, Gao H, Wang J (2018) Models for safety assessment of construction project with some 2-tuple linguistic Pythagorean fuzzy Bonferroni mean operators. IEEE Access 99:52105–52137

    Article  Google Scholar 

  • Ejegwa PA (2019) Pythagorean fuzzy set and its application in career placements based on academic performance using max-min-max composition. Complex Intell Syst 5:165–175

    Article  Google Scholar 

  • Faizi S, Saabun W, Shaheen N, Rehman AU, Wtróbski J (2021) A novel multi-criteria group decision-making approach based on Bonferroni and Heronian mean operators under hesitant 2-tuple linguistic environment. Mathematics 9(13):1489. https://doi.org/10.3390/math9131489

    Article  Google Scholar 

  • Gao JW, Guo FJ, Li XZ, Huang X, Men HJ (2021) Risk assessment of offshore photovoltaic projects under probabilistic linguistic environment. Renew Energy 163:172–187

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Gupta Pankaj, Mehlawat M. Kumar, Grover Nishtha, Pedrycz Witold (2018) Multi-attribute group decision making based on extended TOPSIS method under interval-valued intuitionistic fuzzy environment. Appl Soft Comput 69:554–567

    Article  Google Scholar 

  • Herrera F, Martinez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752

    Article  Google Scholar 

  • Jiao H (2020) Selection of resettlement site in reservoir construction using Pythagorean fuzzy MULTIMOORA multi-criteria decision-making method. J Coast Res 115(1):502–505

    Article  Google Scholar 

  • Karaca C, Ulutas A (2017) Supplier performance evaluation by using SWARA and MULTIMOORA. Econ Manag Econometr 12:137–151

    Google Scholar 

  • Labella L, Dutta B, Martínez L (2021) An optimal best-worst prioritization method under a 2-tuple linguistic environment in decision making. Comput Ind Eng 155:107141. https://doi.org/10.1016/j.cie.2021.107141

    Article  Google Scholar 

  • Liu D, Huang A (2020) Consensus reaching process for fuzzy behavioral TOPSIS method with probabilistic linguistic q-rung orthopair fuzzy set based on correlation measure. Int J Intell Syst 35(3):1–35

    Google Scholar 

  • Ma ZM, Xu ZS (2020) Computation of generalized linguistic term sets based on fuzzy logical algebras for multi-attribute decision making. Granul Comput 5(1):17–28

    Article  Google Scholar 

  • Rodriguez RM, Martinez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119

    Article  Google Scholar 

  • Tehrim ST, Riaz M (2020) An interval-valued bipolar fuzzy linguistic VIKOR method using connection numbers of SPA theory and its application to decision support system. J Intell Fuzzy Syst 39:3931–3948

    Article  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  • Wan SP, Xu GL, Dong JY (2017) Supplier selection using ANP and ELECTRE II in interval 2-tuple linguistic environment. Inf Sci 385:19–38

    Article  Google Scholar 

  • Wan SP, Jin Z, Dong JY (2020) A new order relation for Pythagorean fuzzy numbers and application to multi-attribute group decision making. Knowl Inf Syst 62(2):751–785

    Article  Google Scholar 

  • Wang JQ, Li JJ (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Sci Technol Inf 33(1):8–9

    Google Scholar 

  • Wang HD, He SF, Pan XH (2018) A new bi-directional projection model based on Pythagorean uncertain linguistic variable. Information 9(5):104–116

    Article  Google Scholar 

  • Wang LN, Wang H, Xu ZS, Ren ZL (2019) The interval-valued hesitant Pythagorean fuzzy set and its applications with extended TOPSIS and Choquet integral-based method. Int J Intell Syst 34(6):1063–1085

    Article  Google Scholar 

  • Wang Y, Sun BZ, Zhang XR, Wang Q (2020) BWM and MULTIMOORA-based multigranulation sequential three-way decision model for multi-attribute group decision-making problem. Int J Approx Reason 125:169–186

    Article  MathSciNet  Google Scholar 

  • Wu XL, Liao HC, Xu ZS, Hafezalkotob A, Herrera F (2018) Probabilistic linguistic MULTIMOORA: a multi-criteria decision making method based on the probabilistic linguistic expectation function and the improved Borda rule. IEEE Trans Fuzzy Syst 26:3688–3702

    Article  Google Scholar 

  • Xian SD, Sun WJ (2014) Fuzzy linguistic induced Euclidean OWA distance operator and its application in group linguistic decision making. Int J Intell Syst 29(5):478–491

    Article  Google Scholar 

  • Xian SD, Dong YF, Liu YB, Jing N (2018) A novel approach for linguistic group decision making based on generalized interval-valued intuitionistic fuzzy linguistic induced Hybrid operator and TOPSIS. Int J Intell Syst 33(2):288–314

    Article  Google Scholar 

  • Xue DF, Liu HC (2019) A new approach for emergency decision-making based on zero-sum game with Pythagorean fuzzy uncertain linguistic variables. Int J Intell Syst 34(7):1667–1684

    Article  Google Scholar 

  • Xue WT, Xu ZS, Zhang XL, Tian XL (2018) Pythagorean fuzzy LINMAP method based on the entropy theory for railway project investment decision making. Int J Intell Syst 33(1):93–125

    Article  Google Scholar 

  • Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Article  Google Scholar 

  • Yang W, Pang Y, Shi J (2018) Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR. Neural Comput Appl 29:613–626

    Article  Google Scholar 

  • Yin XP, Xu XH, Pan B (2021) Selection of strategy for large group emergency decision-making based on risk measurement. Reliab Eng Syst Saf 208:107325. https://doi.org/10.1016/j.ress.2020.107325

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Zhang D, Li Y, Wu C (2020) An extended TODIM method to rank products with online reviews under intuitionistic fuzzy environment. J Oper Res Soc 71(2):322–334

    Article  Google Scholar 

  • Zhang Q, Hu J, Feng J (2020) Multiple criteria decision making method based on the new similarity measures of Pythagorean fuzzy set. J Intell Fuzzy Syst 8:1–12

    Google Scholar 

  • Zhu GN, Ma J, Hu J (2021) Evaluating biological inspiration for biologically inspired design: an integrated DEMATEL-MAIRCA based on fuzzy rough numbers. Int J Intell Syst 36(10):6032–6065

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Graduate Teaching Reform Research Program of Chongqing Municipal Education Commission (no. YJG212022) and Chongqing Research and Innovation Project of Graduate Students (no. CYS21326).

Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Sidong Xian & Huilan Pan

  2. School of Automation, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Wenhua Wan

  3. College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Sidong Xian & Xin Li

Authors
  1. Sidong Xian
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Wenhua Wan
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Huilan Pan
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Xin Li
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Sidong Xian.

Additional information

Communicated by Graçaliz Pereira Dimuro.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xian, S., Wan, W., Pan, H. et al. 2-tuple linguistic hesitant Pythagorean fuzzy MULTIMOORA with MSA and its application in the site selection problem of shared vehicle charging pile. Comp. Appl. Math. 41, 213 (2022). https://doi.org/10.1007/s40314-022-01913-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-022-01913-3

Keywords

Mathematics Subject Classification