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AIMS Mathematics

2023, Volume 8, Issue 8: 19240-19263. doi: 10.3934/math.2023981
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Research article

Bipolar complex fuzzy credibility aggregation operators and their application in decision making problem

  • 1.
    Department of Mathematics, Riphah International University Faisalabad Campus, Pakistan
  • 2.
    Department of Mathematics Deanship of Applied Sciences Umm Al-Qura University, Makkah, Saudi Arabia
  • 3.
    Department of Mathematics, Abdul Wali khan University Mardan, KP, Pakistan
  • 4.
    Programme of Mathematics, Faculty of Ocean Engineering Technology and Informatics Universiti Malaysia Terengganu, 21030 Kuala Nerus Terengganu, Malaysia
  • Received: 07 March 2023 Revised: 26 April 2023 Accepted: 01 May 2023 Published: 07 June 2023

  • MSC : 03E72, 47S40

  • A bipolar complex fuzzy credibility set (BCFCS) is a new approach in computational intelligence and decision-making under uncertainty. Bipolar complex fuzzy credibility (BCFC) information has been employed as a strategy for dealing with confusing and unreliable situations that arise in everyday life. In this paper, we used the concept of aggregation operators to diagnose the well-known averaging and geometric aggregation operators, as well as evaluate some properties and related results. Using described operators, an algorithm for multiple criteria group decision making is proposed. Then, a numerical example of a case study of Hospital selection is discussed. Lastly, the comparative analysis of suggested operators with existing operators are also given to discuss the rationality, efficiency and applicability of these operators.

    Citation: Muhammad Qiyas, Muhammad Naeem, Neelam Khan, Lazim Abdullah. Bipolar complex fuzzy credibility aggregation operators and their application in decision making problem[J]. AIMS Mathematics, 2023, 8(8): 19240-19263. doi: 10.3934/math.2023981

    Related Papers:

  • A bipolar complex fuzzy credibility set (BCFCS) is a new approach in computational intelligence and decision-making under uncertainty. Bipolar complex fuzzy credibility (BCFC) information has been employed as a strategy for dealing with confusing and unreliable situations that arise in everyday life. In this paper, we used the concept of aggregation operators to diagnose the well-known averaging and geometric aggregation operators, as well as evaluate some properties and related results. Using described operators, an algorithm for multiple criteria group decision making is proposed. Then, a numerical example of a case study of Hospital selection is discussed. Lastly, the comparative analysis of suggested operators with existing operators are also given to discuss the rationality, efficiency and applicability of these operators.


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    [1] K. T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Set Syst., 33 (1989), 37–45. https://doi.org/10.1016/0165-0114(89)90215-7 doi: 10.1016/0165-0114(89)90215-7
    [2] A. M. D. J. S Alkouri, A. R. Salleh, Complex intuitionistic fuzzy sets, AIP Conference Proceedings, 1482 (2012), 464–470. https://doi.org/10.1063/1.4757515 doi: 10.1063/1.4757515
    [3] A. U. M. Alkouri, A. R. Salleh, Linguistic variable, hedges and several distances on complex fuzzy sets, J. Intell. Fuzzy Syst., 26 (2014), 2527–2535. https://doi.org/10.3233/IFS-130923 doi: 10.3233/IFS-130923
    [4] H. Alolaiyan, H. A. Alshehri, M. H. Mateen, D. Pamucar, M. Gulzar, A novel algebraic structure of ($a, b$)-complex fuzzy subgroups, Entropy, 23 (2021), 992. https://doi.org/10.3390/e23080992 doi: 10.3390/e23080992
    [5] M. Ahsan, M. Saeed, A. Mehmood, M. H. Saeed, J. Asad, The study of HIV diagnosis using complex fuzzy hypersoft mapping and proposing appropriate treatment, IEEE Access, 9 (2021), 104405–104417. https://doi.org/10.1109/ACCESS.2021.3099335 doi: 10.1109/ACCESS.2021.3099335
    [6] A. Al-Husban, Bipolar complex intuitionistic fuzzy sets, Earthline J. Math. Sci., 8 (2022), 273–280. https://doi.org/10.34198/ejms.8222.273280 doi: 10.34198/ejms.8222.273280
    [7] L. Bi, Z. Zeng, B. Hu, S. Dai, Two classes of entropy measures for complex fuzzy sets, Mathematics, 7 (2019), 96. https://doi.org/10.3390/math7010096 doi: 10.3390/math7010096
    [8] S. Dai, L. Bi, B. Hu, Distance measures between the interval-valued complex fuzzy sets, Mathematics, 7 (2019), 549. https://doi.org/10.3390/math7060549 doi: 10.3390/math7060549
    [9] S. Dai, A generalization of rotational invariance for complex fuzzy operations, IEEE Trans. Fuzzy Syst., 29 (2020), 1152–1159. https://doi.org/10.1109/TFUZZ.2020.2969874 doi: 10.1109/TFUZZ.2020.2969874
    [10] S. Greenfield, F. Chiclana, S. Dick, Interval-valued complex fuzzy logic, 2016 IEEE International Conference on Fuzzy Systems, 2016. https://doi.org/10.1109/FUZZ-IEEE.2016.7737939 doi: 10.1109/FUZZ-IEEE.2016.7737939
    [11] H. Garg, D. Rani, Generalized geometric aggregation operators based on t-norm operations for complex intuitionistic fuzzy sets and their application to decision-making, Cogn. Comput., 12 (2020), 679–698. https://doi.org/10.1007/s12559-019-09678-4 doi: 10.1007/s12559-019-09678-4
    [12] H. Garg, D. Rani, Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process, Arab. J. Sci. Eng., 44 (2019), 2679–2698. https://doi.org/10.1007/s13369-018-3413-x doi: 10.1007/s13369-018-3413-x
    [13] H. Gao, M. Lu, Y. Wei, Dual hesitant bipolar fuzzy hamacher aggregation operators and their applications to multiple attribute decision making, J. Intell. Fuzzy Syst., 37 (2019), 5755–5766. https://doi.org/10.3233/JIFS-18266 doi: 10.3233/JIFS-18266
    [14] B. Hu, L. Bi, S. Dai, The orthogonality between complex fuzzy sets and its application to signal detection, Symmetry, 9 (2017), 175. https://doi.org/10.3390/sym9090175 doi: 10.3390/sym9090175
    [15] B. Hu, L. Bi, S. Dai, S. Li, The approximate parallelity of complex fuzzy sets, J. Intell. Fuzzy Syst., 35 (2018), 6343–6351. https://doi.org/10.3233/JIFS-181131 doi: 10.3233/JIFS-181131
    [16] B. Hu, L. Bi, S. Dai, S. Li, Distances of complex fuzzy sets and continuity of complex fuzzy operations, J. Intell. Fuzzy Syst., 35 (2018), 2247–2255. https://doi.org/10.3233/JIFS-172264 doi: 10.3233/JIFS-172264
    [17] G. Huang, L. Xiao, G. Zhang, Assessment and prioritization method of key engineering characteristics for complex products based on cloud rough numbers, Adv. Eng. Inf., 49 (2021), 101309. https://doi.org/10.1016/j.aei.2021.101309 doi: 10.1016/j.aei.2021.101309
    [18] G. Huang, L. Xiao, W. Pedrycz, D. Pamucar, G. Zhang, L. Mart ínez, Design alternative assessment and selection: a novel Z-cloud rough number-based BWM-MABAC model, Inf. Sci., 603 (2022), 149–189. https://doi.org/10.1016/j.ins.2022.04.040 doi: 10.1016/j.ins.2022.04.040
    [19] C. Jana, M. Pal, J. Q. Wang, Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making, Soft Comput., 24 (2020), 3631–3646. https://doi.org/10.1007/s00500-019-04130-z doi: 10.1007/s00500-019-04130-z
    [20] T. Kumar, R. K. Bajaj, On complex intuitionistic fuzzy soft sets with distance measures and entropies, J. Math., 2014 (2014), 972198. https://doi.org/10.1155/2014/972198 doi: 10.1155/2014/972198
    [21] P. Liu, Z. Ali, T. Mahmood, The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making, J. Intell. Fuzzy Syst., 39 (2020), 3351–3374. http://dx.doi.org/10.3233/JIFS-191718 doi: 10.3233/JIFS-191718
    [22] J. Ma, G. Zhang, J. Lu, A method for multiple periodic factor prediction problems using complex fuzzy sets, IEEE Trans. Fuzzy Syst., 20 (2011), 32–45. http://dx.doi.org/10.1109/TFUZZ.2011.2164084 doi: 10.1109/TFUZZ.2011.2164084
    [23] J. M. Merigó, A. M. Gil-Lafuente, D. Yu, C. Llopis-Albert, Fuzzy decision making in complex frameworks with generalized aggregation operators, Appl. Soft Comput., 68 (2018), 314–321. https://doi.org/10.1016/j.asoc.2018.04.002 doi: 10.1016/j.asoc.2018.04.002
    [24] T. Mahmood, Z. Ali, A. Gumaei, Interdependency of complex fuzzy neighborhood operators and derived complex fuzzy coverings, IEEE Access, 9 (2021), 73506–73521. https://doi.org/10.1109/ACCESS.2021.3074590 doi: 10.1109/ACCESS.2021.3074590
    [25] T. Mahmood, U. Ur Rehman, A novel approach towards bipolar complex fuzzy sets and their applications in generalized similarity measures, Int. J. Intell. Syst., 37 (2022), 535–567. https://doi.org/10.1002/int.22639 doi: 10.1002/int.22639
    [26] T. Mahmood, U. Ur Rehman, J. Ahmmad, G. Santos-García, Bipolar complex fuzzy Hamacher aggregation operators and their applications in multi-attribute decision making, Mathematics, 10 (2022), 23. https://doi.org/10.3390/math10010023 doi: 10.3390/math10010023
    [27] T. Mahmood, U. Ur Rehman, A method to multi-attribute decision making technique based on Dombi aggregation operators under bipolar complex fuzzy information, Comput. Appl. Math., 41 (2022), 47. https://doi.org/10.1007/s40314-021-01735-9 doi: 10.1007/s40314-021-01735-9
    [28] D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex fuzzy sets, IEEE Trans. Fuzzy Syst., 10 (2002), 171–186. https://doi.org/10.1109/91.995119 doi: 10.1109/91.995119
    [29] D. Ramot, M. Friedman, G. Langholz, A. Kandel, Complex fuzzy logic, IEEE Trans. Fuzzy Syst., 11 (2003), 450–461. https://doi.org/10.1109/TFUZZ.2003.814832 doi: 10.1109/TFUZZ.2003.814832
    [30] D. Rani, H. Garg, Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making, Expert Syst., 35 (2018), e12325. https://doi.org/10.1111/exsy.12325 doi: 10.1111/exsy.12325
    [31] H. Song, L. Bi, B. Hu, Y. Xu, S. Dai, New distance measures between the interval-valued complex fuzzy sets with applications to decisionmaking, Math. Probl. Eng., 2021 (2021), 6685793. https://doi.org/10.1155/2021/6685793 doi: 10.1155/2021/6685793
    [32] G. Wei, F. E. Alsaadi, T. Hayat, A. Alsaedi, Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making, Int. J. Fuzzy Syst., 20 (2018), 1–12. https://doi.org/10.1007/s40815-017-0338-6 doi: 10.1007/s40815-017-0338-6
    [33] L. Xiao, G. Huang, G. Zhang, An integrated risk assessment method using Z-fuzzy clouds and generalized TODIM, Qual. Reliab. Eng. Int., 38 (2022), 1909–1943. https://doi.org/10.1002/qre.3062 doi: 10.1002/qre.3062
    [34] L. Xiao, G. Huang, W. Pedrycz, D. Pamucar, L. Martínez, G. Zhang, A $q$-rung orthopair fuzzy decision-making model with new score function and best-worst method for manufacturer selection, Inf. Sci., 608 (2022), 153–177. https://doi.org/10.1016/j.ins.2022.06.06 doi: 10.1016/j.ins.2022.06.06
    [35] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353.
    [36] W. R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis, NAFIPS/IFIS/NASA'94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, The Industrial Fuzzy Control and Intellige, San Antonio, TX, USA, 1994,305–309. https://doi.org/10.1109/IJCF.1994.375115
    [37] G. Zhang, T. S. Dillon, K. Y. Cai, J. Ma, J. Lu, Operation properties and $\delta$-equalities of complex fuzzy sets, Int. J. Approx. Reason., 50 (2009), 1227–1249. https://doi.org/10.1016/j.ijar.2009.05.010 doi: 10.1016/j.ijar.2009.05.010
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  • © 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)
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