Research article Special Issues

Combinative distance-based assessment method for decision-making with $ 2 $-tuple linguistic $ q $-rung picture fuzzy sets

  • Received: 25 February 2023 Revised: 31 March 2023 Accepted: 05 April 2023 Published: 12 April 2023
  • Multi-criteria group decision-making (MCGDM) approaches have a substantial effect on decision-making in a range of critical sectors, including science, business, and real-life research. These strategies also efficiently assist researchers in resolving challenges that may arise throughout their study activity. The current work's major purpose is to research and develop the combinative distance-based assessment (CODAS) approach by employing $ 2 $-tuple linguistic $ q $-rung picture fuzzy sets ($ 2 $TL$ q $-RPFSs) as a background. The CODAS technique computes the distances from the negative ideal solutions and ranks the alternatives in increasing order. To compute the normal weights of attributes, the entropy weighting information process is used. Furthermore, two aggregation operators, namely the $ 2 $-tuple linguistic $ q $-rung picture fuzzy Einstein weighted average and the $ 2 $-tuple linguistic $ q $-rung picture fuzzy Einstein order weighted average, are introduced. Our inspiration for employing the notion of $ 2 $TL$ q $-RPFSs is the ability of $ q $-RPFSs to support a wide range of information and the significant qualities of $ 2 $-tuple linguistic term sets to handle qualitative data. Congested transportation networks may be made more efficient by leveraging digital transformation. Real-time traffic management is one solution to the problem of road congestion. As a result of connected autonomous vehicle (CAV) advances, the benefits of real-time traffic management systems have grown dramatically. CAVs can help manage traffic by acting as enforcers. To complement the extended approach, the proposed technique is used to select the best alternative for a real-time traffic management system. The performance of the suggested technique is validated using scenario analysis. The results show that the suggested strategy is efficient and relevant to real-world situations.

    Citation: Ayesha Khan, Uzma Ahmad, Adeel Farooq, Mohammed M. Ali Al-Shamiri. Combinative distance-based assessment method for decision-making with $ 2 $-tuple linguistic $ q $-rung picture fuzzy sets[J]. AIMS Mathematics, 2023, 8(6): 13830-13874. doi: 10.3934/math.2023708

    Related Papers:

  • Multi-criteria group decision-making (MCGDM) approaches have a substantial effect on decision-making in a range of critical sectors, including science, business, and real-life research. These strategies also efficiently assist researchers in resolving challenges that may arise throughout their study activity. The current work's major purpose is to research and develop the combinative distance-based assessment (CODAS) approach by employing $ 2 $-tuple linguistic $ q $-rung picture fuzzy sets ($ 2 $TL$ q $-RPFSs) as a background. The CODAS technique computes the distances from the negative ideal solutions and ranks the alternatives in increasing order. To compute the normal weights of attributes, the entropy weighting information process is used. Furthermore, two aggregation operators, namely the $ 2 $-tuple linguistic $ q $-rung picture fuzzy Einstein weighted average and the $ 2 $-tuple linguistic $ q $-rung picture fuzzy Einstein order weighted average, are introduced. Our inspiration for employing the notion of $ 2 $TL$ q $-RPFSs is the ability of $ q $-RPFSs to support a wide range of information and the significant qualities of $ 2 $-tuple linguistic term sets to handle qualitative data. Congested transportation networks may be made more efficient by leveraging digital transformation. Real-time traffic management is one solution to the problem of road congestion. As a result of connected autonomous vehicle (CAV) advances, the benefits of real-time traffic management systems have grown dramatically. CAVs can help manage traffic by acting as enforcers. To complement the extended approach, the proposed technique is used to select the best alternative for a real-time traffic management system. The performance of the suggested technique is validated using scenario analysis. The results show that the suggested strategy is efficient and relevant to real-world situations.



    加载中


    [1] A. Chehri, H. T. Mouftah, Autonomous vehicles in the sustainable cities, the beginning of a green adventure, Sustain. Cities Soc., 51 (2019), 101751. http://doi.org/10.1016/j.scs.2019.101751 doi: 10.1016/j.scs.2019.101751
    [2] T. G. Molnar, M. Hopka, D. Upadhyay, M. Van Nieuwstadt, G. Orosz, Virtual rings on highways: Traffic control by connected automated vehicles, In: AI-Enabled technologies for autonomous and connected vehicles, Cham: Springer, 2022. http://doi.org/10.1007/978-3-031-06780-8_16
    [3] F. Azadi, Comprehensive arterial traffic control for fully automated and connected vehicles, University of Pittsburgh, PhD thesis, 2022.
    [4] O. Popescu, S. Sha-Mohammad, H. Abdel-Wahab, D. C. Popescu, S. El-Tawab, Automatic incident detection in intelligent transportation systems using aggregation of traffic parameters collected through V2I communications, IEEE Intell. Transp. Syst. Mag., 9 (2017), 64–75. http://doi.org/10.1109/MITS.2017.2666578 doi: 10.1109/MITS.2017.2666578
    [5] C. A. Bojan-Dragos, R. E. Precup, S. Preitl, R. C. Roman, E. L. Hedrea, A. I. Szedlak-Stinean, GWO-based optimal tuning of type-1 and type-2 fuzzy controllers for electromagnetic actuated clutch systems, IFAC-PapersOnline, 54 (2021), 189–194. http://doi.org/10.1016/j.ifacol.2021.10.032 doi: 10.1016/j.ifacol.2021.10.032
    [6] N. Y. Pehlivan, I. B. Turksen, A novel multiplicative fuzzy regression function with a multiplicative fuzzy clustering algorithm, Rom. J. Inf. Sci., 24 (2021), 79–98.
    [7] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353. http://doi.org/10.1142/9789814261302_0021
    [8] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96. http://doi.org/10.1016/S0165-0114(86)80034-3
    [9] R. R. Yager, Pythagorean fuzzy subsets, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, Canada, 2013, 57–61. http://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
    [10] R. R. Yager, Pythagorean membership grades in multi-criteria decision making, IEEE Trans. Fuzzy Syst., 22 (2013), 958–965. http://doi.org/10.1109/TFUZZ.2013.2278989 doi: 10.1109/TFUZZ.2013.2278989
    [11] T. Senapati, R. R. Yager, Fermatean fuzzy sets, J. Ambient Intell. Human. Comput., 11 (2020), 663–674. http://doi.org/10.1007/s12652-019-01377-0
    [12] R. R. Yager, Generalized orthopair fuzzy sets, IEEE Trans. Fuzzy Syst., 26 (2016), 1222–1230. http://doi.org/10.1109/TFUZZ.2016.2604005 doi: 10.1109/TFUZZ.2016.2604005
    [13] B. C. Cuong, V. Kreinovich, Picture fuzzy sets-a new concept for computational intelligence problems, 2013 Third World Congress on Information and Communication Technologies (WICT 2013), Hanoi, Vietnam, 2013, 1–6. http://doi.org/10.1109/WICT.2013.7113099
    [14] F. K. G$\ddot{u}$ndo$\breve{g}$du, C. Kahraman, Spherical fuzzy sets and spherical fuzzy TOPSIS method, J. Intell. Fuzzy Syst., 36 (2019), 337–352. http://doi.org/10.3233/JIFS-181401 doi: 10.3233/JIFS-181401
    [15] T. Mahmood, K. Ullah, Q. Khan, N. Jan, An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets, Neural Comput. Appl., 31 (2019), 7041–7053. http://doi.org/10.1007/s00521-018-3521-2 doi: 10.1007/s00521-018-3521-2
    [16] L. Li, R. T. Zhang, J. Wang, X. P. Shang, K. Y. Bai, A novel approach to multi-attribute group decision-making with $q$-rung picture linguistic information, Symmetry, 10 (2018), 172. http://doi.org/10.3390/sym10050172 doi: 10.3390/sym10050172
    [17] S. H. Gurmani, H. Chen, Y. Bai, Dombi operations for linguistic $T$-spherical fuzzy number: An approach for selection of the best variety of maize, Soft Comput., 26 (2022), 9083–9100. http://doi.org/10.1007/s00500-022-07307-1 doi: 10.1007/s00500-022-07307-1
    [18] S. H. Gurmani, H. Chen, Y. Bai, An extended MABAC method for multiple-attribute group decision making under probabilistic $T$-spherical hesitant fuzzy environment, Kybernetes, 2022, In press. http://doi.org/10.1108/K-01-2022-0137
    [19] C. Lee, B. Hellinga, F. Saccomanno, Evaluation of variable speed limits to improve traffic safety, Transp. Res. Part C: Emerging Technol., 14 (2006), 213–228. http://doi.org/10.1016/j.trc.2006.06.002 doi: 10.1016/j.trc.2006.06.002
    [20] A. Hegyi, B. De Schutter, J. Hellendoorn, Optimal coordination of variable speed limits to suppress shock waves, Transp. Res. Rec., 1852 (2003), 167–174. http://doi.org/10.1109/TITS.2004.842408 doi: 10.1109/TITS.2004.842408
    [21] M. Abdel-Aty, L. Wang, Reducing real-time crash risk for congested expressway weaving segments using ramp metering, 5th IEEE International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS), Naples, Italy, 2017,550–555. http://doi.org/10.1109/MTITS.2017.8005733
    [22] L. Luo, Y. E. Ge, F. Zhang, X. J. Ban, Real-time route diversion control in a model predictive control framework with multiple objectives: Traffic efficiency, emission reduction, and fuel economy, Transp. Res. D: Transp. Environ., 48 (2016), 332–356. http://doi.org/10.1016/j.trd.2016.08.013 doi: 10.1016/j.trd.2016.08.013
    [23] Y. Han, D. Chen, S. Ahn, Variable speed limit control at fixed freeway bottlenecks using connected vehicles, Transp. Res. B: Methodol., 98 (2017), 113–134. http://doi.org/10.1016/j.trb.2016.12.013 doi: 10.1016/j.trb.2016.12.013
    [24] P. Wang, H. Deng, J. Zhang, M. Zhang, Real-time urban regional route planning model for connected vehicles based on V2X communication, J. Transp. Land Use, 13 (2020), 517–538.
    [25] S. R. Bonab, S. J. Ghoushchi, M. Deveci, G. Haseli, Logistic autonomous vehicles assessment using decision support model under spherical fuzzy set integrated Choquet integral approach, Expert Syst. Appl., 214 (2023), 119205. http://doi.org/10.1016/j.eswa.2022.119205 doi: 10.1016/j.eswa.2022.119205
    [26] Z. H. Khattak, B. L. Smith, M. D. Fontaine, Impact of cyberattacks on safety and stability of connected and automated vehicle platoons under lane changes, Accid. Anal. Prev., 150 (2021), 105861. http://doi.org/10.1016/j.aap.2020.105861 doi: 10.1016/j.aap.2020.105861
    [27] Z. H. Khattak, B. L. Smith, H. Park, M. D. Fontaine, Cooperative lane control application for fully connected and automated vehicles at multilane freeways, Transp. Res. Part C: Emerging Technol., 111 (2020), 294–317. http://doi.org/10.1016/j.trc.2019.11.007 doi: 10.1016/j.trc.2019.11.007
    [28] M. Khayatian, M. Mehrabian, A. Shrivastava, RIM: Robust intersection management for connected autonomous vehicles, 2018 IEEE Real-Time Systems Symposium (RTSS), Nashville, USA, 2018, 35–44. http://doi.org/10.1109/RTSS.2018.00014
    [29] A. Talebpour, H. S. Mahmassani, Influence of autonomous and connected vehicles on the stability of traffic flow, Transportation Research Board 94th Annual Meeting, Washington DC, United States, 2015, 15-5971.
    [30] I. Gokasar, D. Pamucar, M. Deveci, W. Ding, A novel rough numbers based extended MACBETH method for the prioritization of the connected autonomous vehicles in real-time traffic management, Expert Syst. Appl., 211 (2023), 118445. http://doi.org/10.1016/j.eswa.2022.118445 doi: 10.1016/j.eswa.2022.118445
    [31] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning Part I, Inf. Sci., 8 (1975), 199–249. http://doi.org/10.1016/0020-0255(75)90036-5 doi: 10.1016/0020-0255(75)90036-5
    [32] F. Herrera, L. Martínez, A $2$-tuple fuzzy linguistic representation model for computing with words, IEEE Trans. Fuzzy Syst., 8 (2000), 746–752. http://doi.org/10.1109/91.890332 doi: 10.1109/91.890332
    [33] F. Herrera, L. Martínez, An approach for combining linguistic and numerical information based on the $2$-tuple fuzzy linguistic representation model in decision-making, Int. J. Uncertain. Fuzziness Knowl.-Based Syst., 8 (2000), 539–562. http://doi.org/10.1142/S0218488500000381 doi: 10.1142/S0218488500000381
    [34] H. Zhang, Linguistic intuitionistic fuzzy sets and application in MAGDM, J. Appl. Math., 2014 (2014), 432092. http://doi.org/10.1155/2014/432092 doi: 10.1155/2014/432092
    [35] H. Garg, Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process, Int. J. Intell. Syst., 33 (2018), 1234–1263. http://doi.org/10.1002/int.21979 doi: 10.1002/int.21979
    [36] M. Lin, X. Li, L. Chen, Linguistic $q$-rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators, Int. J. Intell. Syst., 35 (2020), 217–249. http://doi.org/10.1002/int.22136 doi: 10.1002/int.22136
    [37] X. Deng, J. Wang, G. Wei, Some $2$-tuple linguistic Pythagorean Heronian mean operators and their application to multiple attribute decision-making, J. Exp. Theor. Artif. Intell., 31 (2019), 555–574. http://doi.org/10.1080/0952813X.2019.1579258 doi: 10.1080/0952813X.2019.1579258
    [38] M. Akram, A. Khan, A. Luqman, T. Senapati, D. Pamucar, An extended MARCOS method for MCGDM under $2$-tuple linguistic $q$-rung picture fuzzy environment, Eng. Appl. Artif. Intell., 120 (2023), 105892. http://doi.org/10.1016/j.engappai.2023.105892 doi: 10.1016/j.engappai.2023.105892
    [39] C. L. Hwang, K. Yoon, Multiple attributes decision making methods and applications, Berlin, Heidelberg: Springer, 1981.
    [40] D. Pamucar, G. Cirovic, The selection of transport and handling resources in logistics centers using multi-attributive border approximation area comparison (MABAC), Expert Syst. Appl., 42 (2015), 3016–3028. http://doi.org/10.1016/j.eswa.2014.11.057 doi: 10.1016/j.eswa.2014.11.057
    [41] S. Opricovic, Multicriteria optimization of civil engineering systems, PhD Thesis, Faculty Civil Engineering, Belgrade, 1998.
    [42] M. Lihong, Z. Yanping, Z. Zhiwei, Improved VIKOR algorithm based on AHP and Shannon entropy in the selection of thermal power enterprise's coal suppliers, International Conference on Information Management, Innovation Management and Industrial Engineering, 2 (2008), 129–133. http://doi.org/10.1109/ICIII.2008.29 doi: 10.1109/ICIII.2008.29
    [43] R. E. Bellman, L. A. Zadeh, Decision-making in a fuzzy environment, Manag. Sci., 4 (1970), 141–164. http://doi.org/10.1287/mnsc.17.4.B141 doi: 10.1287/mnsc.17.4.B141
    [44] M. K. Ghorabaee, E. K., Zavadskas, Z. Turskis, J. Antucheviciene, A new combinative distance based assessment (CODAS) method for multi-criteria decision-making, Econ. Comput. Econ. Cybern. Stud. Res., 50 (2016), 25–44.
    [45] F. Lei, G. Wei, X. Chen, Model-based evaluation for online shopping platform with probabilistic double hierarchy linguistic CODAS method, Int. J. Intell. Syst., 36 (2021), 5339–5358. http://doi.org/10.1002/int.22514 doi: 10.1002/int.22514
    [46] V. Simic, S. Karagoz, M. Deveci, N. Aydin, Picture fuzzy extension of the CODAS method for multi-criteria vehicle shredding facility location, Expert Syst. Appl., 175 (2021), 114644. http://doi.org/10.1016/j.eswa.2021.114644 doi: 10.1016/j.eswa.2021.114644
    [47] Q. Wang, Research on teaching quality evaluation of college english based on the CODAS method under interval-valued intuitionistic fuzzy information, J. Intell. Fuzzy Syst., 41 (2021), 1499–1508. http://doi.org/10.3233/JIFS-210366 doi: 10.3233/JIFS-210366
    [48] T. He, S. Zhang, G. Wei, R. Wang, J. Wu, C. Wei, CODAS method for $2$-tuple linguistic Pythagorean fuzzy multiple attribute group decision making and its application to financial management performance assessment, Technol. Econ. Dev. Econ., 26 (2020), 920–932. http://doi.org/10.3846/tede.2020.11970 doi: 10.3846/tede.2020.11970
    [49] S. Naz, M. Akram, A. Sattar, M. M. A. Al-Shamiri, $2$-Tuple linguistic $q$-rung orthopair fuzzy CODAS approach and its application in arc welding robot selection, AIMS Mathematics, 7 (2022), 17529–17569. http://doi.org/10.3934/math.2022966 doi: 10.3934/math.2022966
    [50] S. Vinodh, V. A. Wankhede, Application of fuzzy DEMATEL and fuzzy CODAS for analysis of workforce attributes pertaining to Industry 4.0: A case study, Int. J. Qual. Reliab. Manag., 38 (2021), 1695–1721. http://doi.org/10.1108/IJQRM-09-2020-0322 doi: 10.1108/IJQRM-09-2020-0322
    [51] K. Deveci, R. Cin, A. Kagizman, A modified interval valued intuitionistic fuzzy CODAS method and its application to multi-criteria selection among renewable energy alternatives in Turkey, Appl. Soft Comput., 96 (2020), 106660. http://doi.org/10.1016/j.asoc.2020.106660 doi: 10.1016/j.asoc.2020.106660
    [52] H. Y. Aydogmus, E. Kamber, C. Kahraman, ERP selection using picture fuzzy CODAS method, J. Intell. Fuzzy Syst., 40 (2021), 11363–11373. http://doi.org/10.3233/JIFS-202564 doi: 10.3233/JIFS-202564
    [53] S. Karagoz, M. Deveci, V. Simic, N. Aydin, U. Bolukbas, A novel intuitionistic fuzzy MCDM-based CODAS approach for locating an authorized dismantling center: A case study of Istanbul, Waste Manag. Res., 38 (2020), 660–672. http://doi.org/10.1177/0734242X19899729 doi: 10.1177/0734242X19899729
    [54] A. Karasan, E. Bolt$\ddot{u}$rk, F. K. G$\ddot{u}$ndo$\breve{g}$du, Assessment of livability indices of suburban places of Istanbul by using spherical fuzzy CODAS method, Decision making with spherical fuzzy sets: Theory and applications, Cham: Springer, 2021. http://doi.org/10.1007/978-3-030-45461-6_12
    [55] M. Akram, Z. Niaz, F. Feng, Extended CODAS method for multi-attribute group decision-making based on $2$-tuple linguistic Fermatean fuzzy Hamacher aggregation operators, Granul. Comput., 2022. http://doi.org/10.1007/s41066-022-00332-3
    [56] M. Akram, S. Naz, G. Santos-Garcia, M. R. Saeed, Extended CODAS method for MAGDM with $2$-tuple linguistic $T$-spherical fuzzy sets, AIMS Mathematics, 8 (2023), 3428–3468. http://doi.org/10.3934/math.2023176 doi: 10.3934/math.2023176
    [57] M. Akram, S. Naz, F. Feng, G. Ali, A. Shafiq, Extended MABAC method based on 2-tuple linguistic $T$-spherical fuzzy sets and Heronian mean operators: An application to alternative fuel selection, AIMS Mathematics, 8 (2023), 10619–10653. http://doi.org/10.3934/math.2023539 doi: 10.3934/math.2023539
    [58] X. Peng, Y. Yang, Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators, Int. J. Intell. Syst., 31 (2016), 444–487. http://doi.org/10.1002/int.21790 doi: 10.1002/int.21790
    [59] R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. Syst. Man Cybern., 18 (1988), 183–190. http://doi.org/10.1109/21.87068 doi: 10.1109/21.87068
    [60] H. Gassert, Operators on fuzzy sets: Zadeh and Einstein, Department of Computer Science Information Systems Group, University of Fribourg, Seminar Paper, 2004.
    [61] Z. Xu, Intuitionistic fuzzy aggregation operators, IEEE Trans. Fuzzy Syst., 15 (2007), 1179–1187. http://doi.org/10.1109/TFUZZ.2006.890678 doi: 10.1109/TFUZZ.2006.890678
    [62] G. Deschrijver, C. Cornelis, E. E. Kerre, On the representation of intuitionistic fuzzy $t$-norms and $t$-conorms, IEEE Trans. Fuzzy Syst., 12 (2004), 45–61. http://doi.org/10.1109/TFUZZ.2003.822678 doi: 10.1109/TFUZZ.2003.822678
    [63] H. Garg, Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein $t$-norm and $t$-conorm and their application to decision making, Comput. Ind. Eng., 101 (2016), 53–69. http://doi.org/10.1016/j.cie.2016.08.017 doi: 10.1016/j.cie.2016.08.017
    [64] W. Wang, X. Liu, Intuitionistic fuzzy information aggregation using Einstein operations, IEEE Trans. Fuzzy Syst., 20 (2012), 923–938. http://doi.org/10.1109/TFUZZ.2012.2189405 doi: 10.1109/TFUZZ.2012.2189405
    [65] S. Khan, S. Abdullah, S. Ashraf, Picture fuzzy aggregation information based on Einstein operations and their application in decision making, Math. Sci., 13 (2019), 213–229. http://doi.org/10.1007/s40096-019-0291-7 doi: 10.1007/s40096-019-0291-7
    [66] X. Zhao, G. Wei, Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making, Knowl. Based Syst., 37 (2013), 472–479. http://doi.org/10.1016/j.knosys.2012.09.006 doi: 10.1016/j.knosys.2012.09.006
    [67] P. Liu, P. Wang, Some $q$-rung orthopair fuzzy aggregation operators and their applications to multiple attribute decision making, Int. J. Intell. Syst., 33 (2018), 259–280. http://doi.org/10.1002/int.21927 doi: 10.1002/int.21927
    [68] G. W. Wei, Picture fuzzy aggregation operators and their application to multiple attribute decision making, J. Intell. Fuzzy Syst., 33 (2017), 713–724. http://doi.org/10.3233/JIFS-161798 doi: 10.3233/JIFS-161798
    [69] M. Akram, S. Naz, S. A. Edalatpanah, R. Mehreen, Group decision-making framework under linguistic $q$-rung orthopair fuzzy Einstein models, Soft Comput., 25 (2021), 10309–10334. http://doi.org/10.1007/s00500-021-05771-9 doi: 10.1007/s00500-021-05771-9
    [70] S. Faizi, S. Nawaz, A. Ur-Rehman, Intuitionistic $2$-tuple linguistic aggregation information based on Einstein operations and their applications in group decision making, Artif. Intell. Rev., 53 (2020), 4625–4650. http://doi.org/10.1007/s10462-020-09856-z doi: 10.1007/s10462-020-09856-z
    [71] K. Kumar, S. M. Chen, Multiple attribute group decision making based on advanced linguistic intuitionistic fuzzy weighted averaging aggregation operator of linguistic intuitionistic fuzzy numbers, Inf. Sci., 587 (2022), 813–824. http://doi.org/10.1016/j.ins.2021.11.014 doi: 10.1016/j.ins.2021.11.014
    [72] P. Rani, A. R. Mishra, Fermatean fuzzy Einstein aggregation operators-based MULTIMOORA method for electric vehicle charging station selection, Expert Syst. Appl., 182 (2021), 115267. http://doi.org/10.1016/j.eswa.2021.115267 doi: 10.1016/j.eswa.2021.115267
    [73] B. Sarkar, A. Biswas, Linguistic Einstein aggregation operator-based TOPSIS for multicriteria group decision making in linguistic Pythagorean fuzzy environment, Int. J. Intell. Syst., 36 (2021), 2825–2864. http://doi.org/10.1002/int.22403 doi: 10.1002/int.22403
  • Reader Comments
  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(902) PDF downloads(53) Cited by(0)

Article outline

Figures and Tables

Figures(4)  /  Tables(22)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog