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q-rung orthopair fuzzy bi-direction Choquet integral based on TOPSIS method for multiple attribute group decision making

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Abstract

There exists interrelationship between attributes for multi-attribute group decision making (MAGDM) problems, so capturing correlation among the attributes is necessary. Hence, firstly, the q-rung orthopair fuzzy bi-direction Choquet integral average (q-ROFBDCIA) operator and the q-rung orthopair fuzzy bi-direction exponent Choquet integral geometric (q-ROFBDECIG) operator are introduced to solve decision-making problems (DMPs). These two operators not only define the weight of the attributes but also can depict the relationship between the attributes. Next, the properties and special cases of q-ROFBDCIA and q-ROFBDECIG are shown in detail. And maximizing deviation models to determine fuzzy measure (FM) of decision makers (DMs) and attributes are introduced. Finally, a MAGDM method is established to choose the optical alternative from several alternatives based on the introduced operators and an extended TOPSIS method. A real example is solved by the proposed MAGDM method to exemplify the practicality of the introduced methodology and analyze the superiority of established approach by comparison with other approaches.

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References

  • Akram M, Naz S, Edalatpanah SA, Mehreen R (2021) Group decision-making framework under linguistic q-rung orthopair fuzzy Einstein models. Soft Comput 25:10309–10334

    MATH  Google Scholar 

  • Akram M, Peng XD, Sattar A (2021) A new decision-making model using complex intuitionistic fuzzy Hamacher aggregation operators. Soft Comput 25:7059–7086

    MATH  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(161):1–27

    MathSciNet  MATH  Google Scholar 

  • Ali Z, Mahmood T, Yang MS (2020) TOPSIS method based on complex spherical fuzzy sets with Bonferroni mean operators. Mathematics 8(10):1739

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Aydemir SB, Gunduz SY (2021) A novel approach to multi-attribute group decision making based on power neutrality aggregation operator for q-rung orthopair fuzzy sets. Int J Intell Syst 36(3):1454–1481

    Google Scholar 

  • Bakioglu G, Atahan AO (2021) AHP integrated TOPSIS and VIKOR methods with Pythagorean fuzzy sets to prioritize risks in self-driving vehicles. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2020.106948

    Article  Google Scholar 

  • Bonferroni C (1950) Sulle medie multiple di potenze. Bolletino Matematica Italiana 5(3):267–270

    MathSciNet  MATH  Google Scholar 

  • Chen Y, Li T (2016) Intuitionistic uncertain linguistic information aggregation operators based on Choquet integral and their application. Control Decis 31:842–852

    MATH  Google Scholar 

  • Dimuro GP, Fernandez J, Bedregal B, Mesiar R, Sanz JA, Lucca G (2020) The state-of-art of the generalizations of the Choquet integral: from aggregation and pre-aggregation to ordered directionally monotone functions. Inform Fus 57:27–43

    Google Scholar 

  • Divsalara M, Ahmadi M, Ebrahimi E, Ishizaka A (2022) A probabilistic hesitant fuzzy Choquet integral-based TODIM method for multi-attribute group decision-making. Expert Syst Appl 191:116266

    Google Scholar 

  • Farhadinia B, Effati S, Chiclana F (2021) A family of similarity measures for q-rung orthopair fuzzy sets and their applications to multiple criteria decision making. Int J Intell Syst 36(4):1535–1559

    Google Scholar 

  • Farhadinia B, Aickelin U, Khorshidi HA (2021) Higher order hesitant fuzzy Choquet integral operator and its application to multiple criteria decision making. Iran J Fuzzy Syst 18(1):1–16

    MathSciNet  MATH  Google Scholar 

  • Gao JW, Guo FJ, Ma ZY, Huang X (2021) Multi-criteria decision-making framework for large-scale rooftop photovoltaic project site selection based on intuitionistic fuzzy sets. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2021.107098

    Article  Google Scholar 

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

    Google Scholar 

  • Garg H (2021) CN-q-ROFS: connection number-based q-rung orthopair fuzzy set and their application to decision-making process. Int J Intell Syst 36(5):2229–2266

    Google Scholar 

  • Grabisch G (1995) Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst 69(3):279–298

    MathSciNet  MATH  Google Scholar 

  • Gul M, Ak MF (2021) A modified failure modes and effects analysis using interval-valued spherical fuzzy extension of TOPSIS method: case study in a marble manufacturing facility. Soft Comput 25(8):6157–6178

    Google Scholar 

  • He YD, He Z, Chen HY (2014) Intuitionistic fuzzy interaction Bonferroni means and its application to multiple attribute decision making. IEEE Trans Cybern 45:116–128

    Google Scholar 

  • Hussain A, Ali MI, Mahmood T, Munir M (2020) q-Rung orthopair fuzzy soft average aggregation operators and their application in multicriteria decision-making. Int J Intell Syst 35(4):571–599

    Google Scholar 

  • Hwang CL, Yoon KS (1981) Multiple attribute decision methods and applications. Springer, Berlin

    MATH  Google Scholar 

  • Joshi D, Kumar S (2016) Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making. Eur J Oper Res 248(1):183–191

    MathSciNet  MATH  Google Scholar 

  • Lazim A, Wan RWM (2019) Pythagorean Fuzzy Hamacher Choquet integral operators and their application to multi-criteria decision making. J Intell Fuzzy Syst 37:1259–1274

    Google Scholar 

  • Liang DC, Zhang YRJ, Cao W (2019) q-Rung orthopair fuzzy Choquet integral aggregation and its application in heterogeneous multicriteria two-sided matching decision making. Int J Intell Syst 34:3275–3301

    Google Scholar 

  • Liu PD, Wang P (2018) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280

    Google Scholar 

  • Liu PD, Wang YM (2019) Multiple attribute decision making based on q-rung orthopair fuzzy generalized Maclaurin symmetic mean operators. Inf Sci. https://doi.org/10.1016/j.ins.2020.01.013

    Article  Google Scholar 

  • Liu S, Yu W, Chan FTS, Niu B (2020) A variable weight-based hybrid approach for multi-attribute group decision making under interval-valued intuitionistic fuzzy sets. Int J Intell Syst 36(2):1015–1052

    Google Scholar 

  • Liu Y, Wei GW, Abdullah S, Liu J, Xu L, Liu HB (2021) Banzhaf–Choquet-copula-based aggregation operators for managing q-rung orthopair fuzzy information. Soft Comput 25:6891–6914

    MATH  Google Scholar 

  • Lourenzutti R, Krohling RA, Reformat MZ (2017) Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction. Inf Sci. 408:41–69

    MATH  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 Roy Soc London Ser A 36:59–96

    Google Scholar 

  • Mahmood T, Ali Z (2021) A novel approach of complex q-rung orthopair fuzzy Hamacher aggregation operators and their application for cleaner production assessment in gold mines. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-02697-2

    Article  Google Scholar 

  • Meng FY, Chen YM, Tang J (2020) Multicriteria decision making based on bi-direction Choquet integrals. Inf Sci. https://doi.org/10.1016/j.ins.2020.10.055

    Article  MATH  Google Scholar 

  • Muhammad SAK (2019) The pythagorean fuzzy Einstein Choquet integral operators and their application in group decision making. Comput Appl Math. https://doi.org/10.1007/s40314-019-0871-z

    Article  MathSciNet  MATH  Google Scholar 

  • Muhammad SAK, Saleem A, Muhammad YA, Iqtadar H, Muhammad F (2018) Extension of TOPSIS method base on Choquet integral under interval-valued Pythagorean fuzzy environment. J Intell Fuzzy Syst 34:267–282

    Google Scholar 

  • Nguyen H (2016) A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition. Expert Syst Appl 45:97–107

    Google Scholar 

  • Peng X, Yang Y (2016) Pythagorean fuzzy Choquet integral based MABAC method for multiple attribute group decision making. Int J Intell Syst 31(10):989–1020

    MathSciNet  Google Scholar 

  • Peng XD, Yuan HY (2021) Pythagorean fuzzy multi-criteria decision making method based on multiparametric similarity measure. Cogn Comput 13(2):466–484

    Google Scholar 

  • Peng XD, Huang HH, Luo ZG (2021) q-Rung orthopair fuzzy decision-making framework for integrating mobile edge caching scheme preferences. Int J Intell Syst. https://doi.org/10.1002/int.22377

    Article  Google Scholar 

  • Qin Y, Liu Y, Abdullah S, Wei GW (2021) Group decision support methodology based upon the multigranular generalized orthopair 2-tuple linguistic information model. Int J Intell Syst 36:1–34

    Google Scholar 

  • Qiyas M, Qiyas M, Liu Y, Naeem M (2020) Multi-criteria decision support systems based on linguistic intuitionistic cubic fuzzy aggregation operators. J Ambient Intell Humaniz Comput 12:8285–8303

    Google Scholar 

  • Qiyas M, Abdullah S, Al-Otaibi YD, Aslam M (2021) Generalized interval-valued picture fuzzy linguistic induced hybrid operator and TOPSIS method for linguistic group decision-making. Soft Comput 25(7):5037–5054

    MATH  Google Scholar 

  • Sarkar B, Biswas A (2021) Pythagorean fuzzy AHP-TOPSIS integrated approach for transportation management through a new distance measure. Soft Comput 25(5):4073–4089

    MATH  Google Scholar 

  • Sarkar A, Biswas A (2021) Dual hesitant q-rung orthopair fuzzy Dombi t-conorm and t-norm based Bonferroni mean operators for solving multicriteria group decision making problems. Int J Intell Syst 36(7):3293–3338

    Google Scholar 

  • Sarkar B, Biswas A (2021) Linguistic Einstein aggregation operator-based TOPSIS for multicriteria group decision making in linguistic Pythagorean fuzzy environment. Int J Intell Syst 36(6):2825–2864

    Google Scholar 

  • Singh S, Kumar S (2021) Picture fuzzy Choquet integral-based VIKOR for multicriteria group decision-making problems. Granul Comput. 6:587–601

    Google Scholar 

  • Singh P, Huang YP, Wu SI (2020) An intuitionistic fuzzy set approach for multi-attribute information classification and decision-making. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-020-00879-w

    Article  Google Scholar 

  • Sugeno P (1974) Theory of fuzzy integral and its application. Doctoral dissertation, Tokyo Institute of Technology, Tokyo, Japan

  • Tan CQ (2011) A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS. Expert Syst Appl 38:3023–3033

    Google Scholar 

  • Tan CQ, Chen XH (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37:149–157

    Google Scholar 

  • Tao R, Liu ZY, Cai R, Cheong KH (2021) A dynamic group MCDM model with intuitionistic fuzzy set: perspective of alternative queuing method. Inf Sci 555:85–103

    MathSciNet  MATH  Google Scholar 

  • Wan BT, Huang JL, Chen X (2021) Interval-valued q-rung orthopair fuzzy choquet integral operators and its application in group decision making. Artif Intell

  • Wan BT, Huang JL, Chen X, Cheng YY, Wang J (2022) Interval-valued q-rung orthopair fuzzy Choquet integral operators and their application in group decision-making. Math Problems Eng

  • Wang XT, Triantaphyllou E (2008) Ranking irregularities when evaluating alternatives by using some Electre methods. Omega 36:45–63

    Google Scholar 

  • Wang F, Zhao XD (2021) Prospect-theory and geometric distance measure-based Pythagorean cubic fuzzy multicriteria decision-making. Int J Intell Syst 36:4117–4142

    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 34:1–23

    Google Scholar 

  • Wieczynski JC, Lucca G, Borges EN, Dimuro GP, Lourenzutti R, Bustince H. (2021) CC-separation measure applied in business group decision making. In: 23rd International Conference on Enterprise Information Systems. 1, 452–462

  • Wieczynski JC, Fumanal-Idocin J, Lucca G, Borges EN, Asmus TDC, Emmendorfer L, Bustince H, Dimuro GP (2022) d-XC integrals: on the generalization of the expanded form of the Choquet integral by restricted dissimilarity functions and their applications. IEEE Trans Fuzzy Syst 30:5376–5389

    Google Scholar 

  • Xing YP, Zhang RT, Sun YJ (2018) Some new q-rung orthopair fuzzy point-choquet integral aggregation operators and their application to supplier selection. IEEE 17th Intl Conf. on Cognitive Informatics and Cognitive Computing

  • Xing YP, Zhang RT, Wang J, Bai KY, Xue J (2019) A new multi-criteria group decision-making approach based on q-rung orthopair fuzzy interaction Hamy mean operators. Neural Comput Appl. https://doi.org/10.1007/s00521-019-04269-8

    Article  Google Scholar 

  • Xing YP, Zhang RT, Zhu XM, Bai KY (2019) q-Rung orthopair fuzzy uncertain linguistic Choquet integral operators and their application to multi-attribute decision making. J Intell Fuzzy Syst 37:1123–1139

    Google Scholar 

  • Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180:726–736

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Yager YY (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230

    Google Scholar 

  • Yang ZL, Chang JP (2021) A multi-attribute decision-making-based site selection assessment algorithm for garbage disposal plant using interval q-rung orthopair fuzzy power Muirhead mean operator. Environ Res 193:110385

    Google Scholar 

  • Yang W, Pang YF (2020) New q-rung orthopair fuzzy Bonferroni mean Dombi operators and their application in multiple attribute decision making. IEEE Access 8:50587–50610

    Google Scholar 

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

    MATH  Google Scholar 

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Acknowledgements

This work was supported by Sichuan Province Youth Science and Technology Innovation Team (2019JDTD0015), Application Basic Research Plan Project of Sichuan Province (2021JY0108), Scientifc Research Project of Neijiang Normal University (18TD08), Scientifc Research Project of Neijiang Normal University (2019YB11), Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province (DRN19014), Scientific Research Project of Neijiang City(NJFH20-003).

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  1. Hongjuan Wang and Yi Liu contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Information Sciences, Numerical Simulation Key Laboratory of Sichuan Provincial Universities, Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang, 641000, Sichuan, China

    Hongjuan Wang & Yi Liu

  2. School of Business, Sichuan Normal University, Chengdu, 610101, Sichuan, China

    ChunYu Zhao

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  1. Hongjuan Wang
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  2. Yi Liu
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Correspondence to Hongjuan Wang.

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Wang, H., Liu, Y. & Zhao, C. q-rung orthopair fuzzy bi-direction Choquet integral based on TOPSIS method for multiple attribute group decision making. Comp. Appl. Math. 42, 105 (2023). https://doi.org/10.1007/s40314-023-02222-z

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