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Complex pythagorean fuzzy aggregation operators based on confidence levels and their applications


  • Received: 16 October 2021 Accepted: 17 November 2021 Published: 29 November 2021
  • The most important influence of this assessment is to analyze some new operational laws based on confidential levels (CLs) for complex Pythagorean fuzzy (CPF) settings. Moreover, to demonstrate the closeness between finite numbers of alternatives, the conception of confidence CPF weighted averaging (CCPFWA), confidence CPF ordered weighted averaging (CCPFOWA), confidence CPF weighted geometric (CCPFWG), and confidence CPF ordered weighted geometric (CCPFOWG) operators are invented. Several significant features of the invented works are also diagnosed. Moreover, to investigate the beneficial optimal from a large number of alternatives, a multi-attribute decision-making (MADM) analysis is analyzed based on CPF data. A lot of examples are demonstrated based on invented works to evaluate the supremacy and ability of the initiated works. For massive convenience, the sensitivity analysis and merits of the identified works are also explored with the help of comparative analysis and they're graphical shown.

    Citation: Tahir Mahmood, Zeeshan Ali, Kifayat Ullah, Qaisar Khan, Hussain AlSalman, Abdu Gumaei, Sk. Md. Mizanur Rahman. Complex pythagorean fuzzy aggregation operators based on confidence levels and their applications[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 1078-1107. doi: 10.3934/mbe.2022050

    Related Papers:

  • The most important influence of this assessment is to analyze some new operational laws based on confidential levels (CLs) for complex Pythagorean fuzzy (CPF) settings. Moreover, to demonstrate the closeness between finite numbers of alternatives, the conception of confidence CPF weighted averaging (CCPFWA), confidence CPF ordered weighted averaging (CCPFOWA), confidence CPF weighted geometric (CCPFWG), and confidence CPF ordered weighted geometric (CCPFOWG) operators are invented. Several significant features of the invented works are also diagnosed. Moreover, to investigate the beneficial optimal from a large number of alternatives, a multi-attribute decision-making (MADM) analysis is analyzed based on CPF data. A lot of examples are demonstrated based on invented works to evaluate the supremacy and ability of the initiated works. For massive convenience, the sensitivity analysis and merits of the identified works are also explored with the help of comparative analysis and they're graphical shown.



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    [1] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353. doi: 10.1016/S0019-9958(65)90241-X. doi: 10.1016/S0019-9958(65)90241-X
    [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96. doi: 10.1016/S0165-0114(86)80034-3. doi: 10.1016/S0165-0114(86)80034-3
    [3] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. doi: 10.1016/S0898-1221(99)00056-5. doi: 10.1016/S0898-1221(99)00056-5
    [4] F. Fatimah, D. Rosadi, R. F. Hakim, J. C. R. Alcantud, N-soft sets and their decision making algorithms, Soft Comput., 22 (2018), 3829–3842. doi: 10.1007/s00500-017-2838-6. doi: 10.1007/s00500-017-2838-6
    [5] M. Akram, A. Adeel, J. C. R. Alcantud, Fuzzy N-soft sets: A novel model with applications, J. Intell. Fuzzy Syst., 35 (2018), 4757–4771. doi: 10.3233/JIFS-18244. doi: 10.3233/JIFS-18244
    [6] M. Akram, G. Ali, J. C. Alcantud, F. Fatimah, Parameter reductions in N‐soft sets and their applications in decision‐making, Expert Syst., 38 (2021), e12601. doi: 10.1111/exsy.12601. doi: 10.1111/exsy.12601
    [7] M. Akram, A. Adeel, J. C. R. Alcantud, Group decision-making methods based on hesitant N-soft sets, Expert Syst. Appl., 115 (2019), 95–105. doi: 10.1016/j.eswa.2018.07.060. doi: 10.1016/j.eswa.2018.07.060
    [8] K. M. Lee, Bipolar valued fuzzy sets and their operations, Proc. Int. Conf. Intell. Technol., Bangkok, Thailand, (2000), 307–312.
    [9] T. Mahmood, A novel approach towards bipolar soft sets and their applications, J. Math., 2020 (2020), 4690808. doi: 10.1155/2020/4690808.
    [10] R. R. Yager, Pythagorean fuzzy subsets, in 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), (2013), 57–61. doi: 10.1109/IFSA-NAFIPS.2013.6608375.
    [11] P. A. Ejegwa, S. Wen, Y. Feng, W. Zhang, J. Chen, Some new Pythagorean fuzzy correlation techniques via statistical viewpoint with applications to decision-making problems, J. Intell. Fuzzy Syst., (2021) (Preprint), 1–13. doi: 10.3233/JIFS-202469.
    [12] M. Gul, Application of Pythagorean fuzzy AHP and VIKOR methods in occupational health and safety risk assessment: the case of a gun and rifle barrel external surface oxidation and colouring unit, Int. J. Occup. Saf. Ergon., 7 (2018), 705–718. doi: 10.1080/10803548.2018.1492251. doi: 10.1080/10803548.2018.1492251
    [13] K. Naeem, M. Riaz, D. Afzal, Pythagorean m-polar Fuzzy Sets and TOPSIS method for the Selection of Advertisement Mode, J. Intell. Fuzzy Syst., 37 (2019), 8441–8458. doi: 10.3233/JIFS-191087. doi: 10.3233/JIFS-191087
    [14] M. Riaz, K. Naeem, D. Afzal, Pythagorean m-polar fuzzy soft sets with TOPSIS method for MCGDM, Punjab Uni. J. Math., 52 (2020), 21–46.
    [15] T. Y. Chen, New Chebyshev distance measures for Pythagorean fuzzy sets with applications to multiple criteria decision analysis using an extended ELECTRE approach, Expert Syst. Appl., 147 (2020), 113164. doi: 10.1016/j.eswa.2019.113164. doi: 10.1016/j.eswa.2019.113164
    [16] D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex fuzzy sets, IEEE Trans. Fuzzy Syst., 10 (2002), 171–186. doi: 10.1109/91.995119. doi: 10.1109/91.995119
    [17] A. M. J. S. Alkouri, A. R. Salleh, Complex intuitionistic fuzzy sets, in AIP conference proceedings, 1482 (2021), 464–470. doi: 10.1063/1.4757515.
    [18] M. Ali, D. E. Tamir, N. D. Rishe, A. Kandel, Complex intuitionistic fuzzy classes, in 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), (2016), 2027–2034. doi: 10.1109/FUZZ-IEEE.2016.7737941.
    [19] N. Yaqoob, M. Gulistan, S. Kadry, H. A. Wahab, Complex intuitionistic fuzzy graphs with application in cellular network provider companies, Mathematics, 7 (2019), 35. doi: 10.3390/math7010035. doi: 10.3390/math7010035
    [20] T. Kumar, R. K. Bajaj, On complex intuitionistic fuzzy soft sets with distance measures and entropies, J. Math., 2014 (2014). doi: 10.1155/2014/972198.
    [21] H. Garg, D. Rani, Novel aggregation operators and ranking method for complex intuitionistic fuzzy sets and their applications to decision-making process, Artif. Intell. Rev., (2019), 1–26. doi: 10.1007/s10462-019-09772-x. doi: 10.1007/s10462-019-09772-x
    [22] R. T. Ngan, M. Ali, D. E. Tamir, N. D. Rishe, A. Kandel, Representing complex intuitionistic fuzzy set by quaternion numbers and applications to decision making, Appl. Soft Comput., 87 (2020), 105961. doi: 10.1016/j.asoc.2019.105961. doi: 10.1016/j.asoc.2019.105961
    [23] M. Gulzar, M. H. Mateen, D. Alghazzawi, N. Kausar, A novel applications of complex intuitionistic fuzzy sets in group theory, IEEE Access, 8 (2020), 196075–196085. doi: 10.1109/ACCESS.2020.3034626. doi: 10.1109/ACCESS.2020.3034626
    [24] S. G. Quek, G. Selvachandran, B. Davvaz, M. Pal, The algebraic structures of complex intuitionistic fuzzy soft sets associated with groups and subgroups, Sci. Iran., 26 (2019), 1898–1912.
    [25] K. Ullah, T. Mahmood, Z. Ali, N. Jan, On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition, Complex Intell. Syst., 6 (2020), 15–27. doi: 10.1007/s40747-019-0103-6. doi: 10.1007/s40747-019-0103-6
    [26] M. Akram, S. Naz, A novel decision-making approach under complex Pythagorean fuzzy environment, Math. Comput. Appl., 24 (2019), 73. doi: 10.3390/mca24030073. doi: 10.3390/mca24030073
    [27] M. Akram, A. Sattar, Competition graphs under complex Pythagorean fuzzy information, J. Appl. Math. Comput., 63 (2020), 543–583. doi: 10.1007/s12190-020-01329-4. doi: 10.1007/s12190-020-01329-4
    [28] M. Akram, A. Khan, A. B. Saeid, Complex Pythagorean Dombi fuzzy operators using aggregation operators and their decision‐making, Expert Syst., (2020), e12626. doi: 10.1111/exsy.12626. doi: 10.1111/exsy.12626
    [29] X. Ma, M. Akram, K. Zahid, J. C. R. Alcantud, Group decision-making framework using complex Pythagorean fuzzy information, Neural Comput. Appl., (2020), 1–21. doi: 10.1007/s00521-020-05100-5. doi: 10.1007/s00521-020-05100-5
    [30] M. Akram, A. Khan, Complex Pythagorean Dombi fuzzy graphs for decision making, Granular Comput., (2020), 1–25. doi: 10.1007/s41066-018-0132-3. doi: 10.1007/s41066-018-0132-3
    [31] H. Garg, Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process, Comput. Math. Organ. Theory, 23 (2017), 546–571. doi: 10.1007/s10588-017-9242-8. doi: 10.1007/s10588-017-9242-8
    [32] W. Wang, X. Liu, Intuitionistic fuzzy geometric aggregation operators based on Einstein operations, Int. J. Intell. Syst., 26 (2011), 1049–1075. doi: 10.1002/int.20498. doi: 10.1002/int.20498
    [33] J. Y. Huang, Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, J. Intell. Fuzzy Syst., 27 (2014), 505–513. doi: 10.3233/IFS-131019. doi: 10.3233/IFS-131019
    [34] X. Zhang, P. Liu, Y. Wang, Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators, J. Intell. Fuzzy Syst., 29 (2015), 2235–2246. doi: 10.3233/IFS-151699. doi: 10.3233/IFS-151699
    [35] P. Liu, S. M. Chen, Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers, IEEE Trans. Cybern., 47 (2016), 2514–2530. doi: 10.1109/TCYB.2016.2634599. doi: 10.1109/TCYB.2016.2634599
    [36] S. Das, D. Guha, Family of harmonic aggregation operators under intuitionistic fuzzy environment, Sci. Iran. Trans. E, Ind. Eng., 24 (2017), 3308–3323.
    [37] Z. Xu, R. R. Yager, Intuitionistic fuzzy Bonferroni means, IEEE Trans. Syst., Man, Cybern., 41 (2010), 568–578. doi: 10.1109/TSMCB.2010.2072918. doi: 10.1109/TSMCB.2010.2072918
    [38] X. Yu, Z. Xu, Prioritized intuitionistic fuzzy aggregation operators, Inf. Fusion, 14 (2013), 108–116. doi: 10.1016/j.inffus.2012.01.011. doi: 10.1016/j.inffus.2012.01.011
    [39] W. Jiang, B. Wei, X. Liu, X. Li, H. Zheng, Intuitionistic fuzzy power aggregation operator based on entropy and its application in decision making, Int. J.Intell. Syst., 33 (2018), 49–67. doi: 10.1002/int.21939. doi: 10.1002/int.21939
    [40] J. Qin, X. Liu, An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators, J.Intell. Fuzzy Syst., 27 (2014), 2177–2190. doi: 10.3233/IFS-141182. doi: 10.3233/IFS-141182
    [41] X. Peng, H. Yuan, Fundamental properties of Pythagorean fuzzy aggregation operators, Fundam. Informaticae, 147 (2016), 415–446. doi: 10.3233/FI-2016-1415. doi: 10.3233/FI-2016-1415
    [42] H. Garg, Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t‐norm and t‐conorm for multicriteria decision‐making process, Int. J. Intell. Syst., 32 (2017), 597–630. doi: 10.1002/int.21860. doi: 10.1002/int.21860
    [43] S. J. Wu, G. W. Wei, Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, Int. J. Knowl.-based Intell. Eng. Syst., 21 (2017), 189–201. doi: 10.3233/KES-170363. doi: 10.3233/KES-170363
    [44] Y. Xing, R. Zhang, J. Wang, X. Zhu, Some new Pythagorean fuzzy Choquet-Frank aggregation operators for multi‐attribute decision making, Int. J. Intell. Syst., 33 (2018), 2189–2215. doi: 10.1002/int.22025. doi: 10.1002/int.22025
    [45] Z. Li, G. Wei, Pythagorean fuzzy heronian mean operators in multiple attribute decision making and their application to supplier selection, Int. J. Knowl.-Based Intell. Eng. Syst., 23 (2019), 77–91. doi: 10.3233/KES-190401. doi: 10.3233/KES-190401
    [46] D. Liang, Y. Zhang, Z. Xu, A. P. Darko, Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading, Int. J. Intell. Syst., 33 (2018), 615–633. doi: 10.1002/int.21960. doi: 10.1002/int.21960
    [47] M. S. A. Khan, S. Abdullah, A. Ali, F. Amin, Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making, Granular Comput., 4 (2019), 249–263. doi: 10.1007/s41066-018-0093-6. doi: 10.1007/s41066-018-0093-6
    [48] G. Wei, M. Lu, Pythagorean fuzzy power aggregation operators in multiple attribute decision making, Int. J. Intell. Syst., 33 (2018), 169–186. doi: 10.1002/int.21946. doi: 10.1002/int.21946
    [49] G. Wei, M. Lu, Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making, Int. J. Intell. Syst., 33 (2018), 1043–1070. doi: 10.1002/int.21911. doi: 10.1002/int.21911
    [50] K. Rahman, S. Ayub, S. Abdullah, Generalized intuitionistic fuzzy aggregation operators based on confidence levels for group decision making, Granular Comput., 6 (2021), 867–886. doi: 10.1007/s41066-020-00235-1. doi: 10.1007/s41066-020-00235-1
    [51] Z. Ali, T. Mahmood, Maclaurin symmetric mean operators and their applications in the environment of complex q-rung orthopair fuzzy sets, Comput. Appl. Math., 39 (2020), 1–27. doi: 10.1007/s40314-020-01145-3. doi: 10.1007/s40314-020-01145-3
    [52] T. Mahmood, Z. Ali, Entropy measure and TOPSIS method based on correlation coefficient using complex q-rung orthopair fuzzy information and its application to multi-attribute decision making, Soft Comput., 25 (2021), 1249–1275. doi: 10.1007/s00500-020-05218-7. doi: 10.1007/s00500-020-05218-7
    [53] M. Akram, C. Kahraman, K. Zahid, Group decision-making based on complex spherical fuzzy VIKOR approach, Knowl.-Based Syst., 216 (2021), 106793. doi: 10.1016/j.knosys.2021.106793. doi: 10.1016/j.knosys.2021.106793
    [54] Z. Ali, T. Mahmood, M. S. Yang, TOPSIS method based on complex spherical fuzzy sets with Bonferroni mean operators, Mathematics, 8 (2020), 1739. doi: 10.3390/math8101739. doi: 10.3390/math8101739
    [55] 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. doi: 10.1007/s00521-018-3521-2. doi: 10.1007/s00521-018-3521-2
    [56] K. Ullah, Picture fuzzy maclaurin symmetric mean operators and their applications in solving multiattribute decision-making problems, Math. Probl. Eng., 2021 (2021), 1098631. doi: 10.1155/2021/1098631. doi: 10.1155/2021/1098631
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