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AIMS Mathematics

2023, Volume 8, Issue 5: 11916-11942. doi: 10.3934/math.2023602
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Research article

Sine hyperbolic fractional orthotriple linear Diophantine fuzzy aggregation operator and its application in decision making

  • 1.
    Department of Mathematics Deanship of Applied Sciences Umm Al-Qura University, Makkah, Saudi Arabia
  • 2.
    Department of Mathematics, Riphah International University Faisalabad Campus, Pakistan
  • 3.
    Programme of Mathematics, Faculty of Ocean Engineering Technology and Informatics Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia
  • 4.
    Department of Mathematics, Abdul Wali khan University Mardan, KP, Pakistan
  • Received: 29 December 2022 Revised: 27 February 2023 Accepted: 02 March 2023 Published: 20 March 2023

  • MSC : 03E72, 47S40

  • The idea of sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs), which allows more uncertainty than fractional orthotriple fuzzy sets (FOFSs) is noteworthy. The regularity and symmetry of the origin are maintained by the widely recognized sine hyperbolic function, which satisfies the experts' expectations for the properties of the multi-time process. Compared to fractional orthotriple linear Diophantine fuzzy sets, sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs) provide a significant idea for enabling more uncertainty. The objective of this research is to provide some reliable sine hyperbolic operational laws for FOLDFSs in order to sustain these properties and the significance of sinh-FOLDFSs. Both the accuracy and score functions for the sinh-FOLDFSs are defined. We define a group of averaging and geometric aggregation operators on the basis of algebraic t-norm and t-conorm operations. The basic characteristics of the defined operators are studied. Using the specified aggregation operators, a group decision-making method for solving real-life decision-making problem is proposed. To verify the validity of the proposed method, we compare our method with other existing methods.

    Citation: Muhammad Naeem, Muhammad Qiyas, Lazim Abdullah, Neelam Khan. Sine hyperbolic fractional orthotriple linear Diophantine fuzzy aggregation operator and its application in decision making[J]. AIMS Mathematics, 2023, 8(5): 11916-11942. doi: 10.3934/math.2023602

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  • The idea of sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs), which allows more uncertainty than fractional orthotriple fuzzy sets (FOFSs) is noteworthy. The regularity and symmetry of the origin are maintained by the widely recognized sine hyperbolic function, which satisfies the experts' expectations for the properties of the multi-time process. Compared to fractional orthotriple linear Diophantine fuzzy sets, sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs) provide a significant idea for enabling more uncertainty. The objective of this research is to provide some reliable sine hyperbolic operational laws for FOLDFSs in order to sustain these properties and the significance of sinh-FOLDFSs. Both the accuracy and score functions for the sinh-FOLDFSs are defined. We define a group of averaging and geometric aggregation operators on the basis of algebraic t-norm and t-conorm operations. The basic characteristics of the defined operators are studied. Using the specified aggregation operators, a group decision-making method for solving real-life decision-making problem is proposed. To verify the validity of the proposed method, we compare our method with other existing methods.


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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] M. I. Ali, Another view on q-rung orthopair fuzzy sets, Int. J. Intell. Syst., 33 (2018), 2139–2153. https://doi.org/10.1002/int.22007 doi: 10.1002/int.22007
    [3] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, J. Intell. Fuzzy Syst., 36 (2019), 2829–2844. https://doi.org/10.3233/JIFS-172009 doi: 10.3233/JIFS-172009
    [4] S. Ashraf, S. Abdullah, M. Aslam, M. Qiyas, M. A. Kutbi, Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms, J. Intell. Fuzzy Syst., 36 (2019), 6089–6102. https://doi.org/10.3233/JIFS-181941 doi: 10.3233/JIFS-181941
    [5] A. Albu, R. E. Precup, T. A. Teban, Results and challenges of artificial neural networks used for decision-making and control in medical applications, Facta Univ., Ser.: Mech. Eng., 17 (2019), 285–308. https://doi.org/10.22190/FUME190327035A doi: 10.22190/FUME190327035A
    [6] S. S. Abosuliman, S. Abdullah, M. Qiyas, Three-way decisions making using covering based fractional Orthotriple fuzzy rough set model, Mathematics, 8 (2020), 1121. https://doi.org/10.3390/math8071121 doi: 10.3390/math8071121
    [7] A. Calik, A novel Pythagorean fuzzy AHP and fuzzy TOPSIS methodology for green supplier selection in the Industry 4.0 era, Soft Comput., 25 (2021), 2253–2265. https://doi.org/10.1007/s00500-020-05294-9 doi: 10.1007/s00500-020-05294-9
    [8] H. Garg, A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making, Int. J. Intell. Syst., 31 (2016), 886–920. https://doi.org/10.1002/int.21809 doi: 10.1002/int.21809
    [9] H. Garg, S. M. Chen, Multi-attribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets, Inf. Sci., 517 (2020), 427–447. https://doi.org/10.1016/j.ins.2019.11.035 doi: 10.1016/j.ins.2019.11.035
    [10] S. Ghosh, S. K. Roy, Fuzzy-rough multi-objective product blending fixed-charge transportation problem with truck load constraints through transfer station, RAIRO: Oper. Res., 55 (2021), S2923–S2952. https://doi.org/10.1051/ro/2020129 doi: 10.1051/ro/2020129
    [11] S. Ghosh, S. K. Roy, A. Ebrahimnejad, J. L. Verdegay, Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem, Complex Intell. Syst., 7 (2021), 1009–1023. https://doi.org/10.1007/s40747-020-00251-3 doi: 10.1007/s40747-020-00251-3
    [12] M. R. Hashmi, S. T. Tehrim, M. Riaz, D. Pamucar, G. Cirovic, Spherical linear diophantine fuzzy soft rough sets with multi-criteria decision making, Axioms, 10 (2021), 185. https://doi.org/10.3390/axioms10030185 doi: 10.3390/axioms10030185
    [13] M. Z. Hanif, N. Yaqoob, M. Riaz, M. Aslam, Linear Diophantine fuzzy graphs with new decision-making approach, AIMS Math., 7 (2022), 14532–14556. https://doi.org/10.3934/math.2022801 doi: 10.3934/math.2022801
    [14] S. Ketsarapong, V. Punyangarm, K. Phusavat, B. Lin, An experience-based system supporting inventory planning: a fuzzy approach, Expert Syst. Appl., 39 (2012), 6994–7003. https://doi.org/10.1016/j.eswa.2012.01.048 doi: 10.1016/j.eswa.2012.01.048
    [15] F. Kutlu Gundogdu, C. Kahraman, Spherical fuzzy sets and spherical fuzzy TOPSIS method, J. Intell. Fuzzy Syst., 36 (2019), 337–352. https://doi.org/10.3233/JIFS-181401 doi: 10.3233/JIFS-181401
    [16] Q. Lei, Z. Xu, Relationships between two types of intuitionistic fuzzy definite integrals, IEEE Trans. Fuzzy Syst., 24 (2016), 1410–1425. https://doi.org/10.1109/TFUZZ.2016.2516583 doi: 10.1109/TFUZZ.2016.2516583
    [17] 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. https://doi.org/10.1002/int.21927 doi: 10.1002/int.21927
    [18] Z. Liu, S. Wang, P. Liu, Multiple attribute group decision making based on q-rung orthopair fuzzy Heronian mean operators, Int. J. Intell. Syst., 33 (2018), 2341–2363. https://doi.org/10.1002/int.22032 doi: 10.1002/int.22032
    [19] C. C. Li, Y. Dong, H. Liang, W. Pedrycz, F. Herrera, Data-driven method to learning personalized individual semantics to support linguistic multi-attribute decision making, Omega, 111 (2022), 102642. https://doi.org/10.1016/j.omega.2022.102642 doi: 10.1016/j.omega.2022.102642
    [20] D. Mardanya, G. Maity, S. K. Roy, Solving bi-level multi-objective transportation problem under fuzziness, Int. J. Uncertain. Fuzz., 29 (2021), 411–433. https://doi.org/10.1142/S0218488521500185 doi: 10.1142/S0218488521500185
    [21] S. Midya, S. K. Roy, F. Y. Vincent, Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain, Int. J. Mach. Learn. Cyber., 12 (2021), 699–717. https://doi.org/10.1007/s13042-020-01197-1 doi: 10.1007/s13042-020-01197-1
    [22] M. M. S. Mohammad, S. Abdullah, M. M. Al-Shomrani, Some linear Diophantine fuzzy similarity measures and their application in decision making problem, IEEE Access, 10 (2022), 29859–29877. https://doi.org/10.1109/access.2022.3151684 doi: 10.1109/access.2022.3151684
    [23] M. Naeem, M. Qiyas, M. M. Al-Shomrani, S. Abdullah, Similarity measures for fractional orthotriple fuzzy sets using cosine and cotangent functions and their application in accident emergency response, Mathematics, 8 (2020), 1653. https://doi.org/10.3390/math8101653 doi: 10.3390/math8101653
    [24] X. Peng, Y. Yang, Some results for Pythagorean fuzzy sets, Inter. J. Intell. Syst., 30 (2015), 1133–1160. https://doi.org/10.1002/int.21738 doi: 10.1002/int.21738
    [25] M. Qiyas, S. Abdullah, F. Khan, M. Naeem, Banzhaf-Choquet-Copula-based aggregation operators for managing fractional orthotriple fuzzy information, Alex. Eng. J., 61 (2022), 4659–4677. https://doi.org/10.1016/j.aej.2021.10.029 doi: 10.1016/j.aej.2021.10.029
    [26] M. Qiyas, M. Naeem, S. Abdullah, F. Khan, N. Khan, H. Garg, Fractional orthotriple fuzzy rough Hamacher aggregation operators and-their application on service quality of wireless network selection, Alex. Eng. J., 61 (2022), 10433–10452. https://doi.org/10.1016/j.aej.2022.03.002 doi: 10.1016/j.aej.2022.03.002
    [27] M. Qiyas, S. Abdullah, N. Khan, M. Naeem, F. Khan, Y. Liu, Case study for hospital-based Post-Acute Care-Cerebrovascular disease using Sine hyperbolic q-rung orthopair fuzzy Dombi aggregation operators, Expert Syst. Appl., 215 (2023), 119224. https://doi.org/10.1016/j.eswa.2022.119224 doi: 10.1016/j.eswa.2022.119224
    [28] M. Qiyas, M. Naeem, L. Abdullah, M. Riaz, N. Khan, Decision support system based on complex fractional orthotriple fuzzy 2-tuple linguistic aggregation operator, Symmetry, 15 (2023), 251. https://doi.org/10.3390/sym15010251 doi: 10.3390/sym15010251
    [29] M. Qiyas, M. Naeem, N. Khan, Fractional orthotriple fuzzy Choquet-Frank aggregation operators and their application in optimal selection for EEG of depression patients, AIMS Math., 8 (2023), 6323–6355. https://doi.org/10.3934/math.2023320 doi: 10.3934/math.2023320
    [30] M. Z. Reformat, R. R. Yager, Suggesting recommendations using Pythagorean fuzzy sets illustrated using Netix movie data, In: International conference on information processing and management of uncertainty in knowledge-based systems, 2014,546–556. https://doi.org/10.1007/978-3-319-08795-5_56
    [31] M. Riaz, M. R. Hashmi, Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems, J. Intell. Fuzzy Syst., 37 (2019), 5417–5439. https://doi.org/10.3233/JIFS-190550 doi: 10.3233/JIFS-190550
    [32] M. Riaz, M. R. Hashmi, H. Kalsoom, D. Pamucar, Y. M. Chu, Linear Diophantine fuzzy soft rough sets for the selection of sustainable material handling equipment, Symmetry, 12 (2020), 1215. https://doi.org/10.3390/sym12081215 doi: 10.3390/sym12081215
    [33] M. Riaz, M. R. Hashmi, D. Pamucar, Y. M. Chu, Spherical linear Diophantine fuzzy sets with modeling uncertainties in MCDM, Comput. Model. Eng. Sci., 126 (2021), 1125–1164. https://doi.org/10.32604/cmes.2021.013699 doi: 10.32604/cmes.2021.013699
    [34] G. Wei, H. Gao, Y. Wei, Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making, Int. J. Intell. Syst., 33 (2018), 1426–1458. https://doi.org/10.1002/int.21985 doi: 10.1002/int.21985
    [35] S. Wang, J. Wu, F. Chiclana, Q. Sun, E. Herrera-Viedma, Two-stage feedback mechanism with different power structures for consensus in large-scale group decision making, IEEE Trans. Fuzzy Syst., 30 (2022), 4177–4189. https://doi.org/10.1109/TFUZZ.2022.3144536 doi: 10.1109/TFUZZ.2022.3144536
    [36] Z. Xu, J. Qin, J. Liu, L. Martinez, Sustainable supplier selection based on AHPSort Ⅱ in interval type-2 fuzzy environment, Inf. Sci., 483 (2019), 273–293. https://doi.org/10.1016/j.ins.2019.01.013 doi: 10.1016/j.ins.2019.01.013
    [37] Y. Xing, R. Zhang, Z. Zhou, J. Wang, Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making, Soft Comput., 23 (2019), 11627–11649. https://doi.org/10.1007/s00500-018-03712-7 doi: 10.1007/s00500-018-03712-7
    [38] Y. Xing, J. Wu, F. Chiclana, G. Yu, M. Cao, E. Herrera-Viedma, A bargaining game based feedback mechanism to support consensus in dynamic social network group decision making, Inf. Fusion, 93 (2023), 363–382. https://doi.org/10.1016/j.inffus.2023.01.004 doi: 10.1016/j.inffus.2023.01.004
    [39] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst., 22 (2013), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989 doi: 10.1109/TFUZZ.2013.2278989
    [40] R. R. Yager, Generalized orthopair fuzzy sets, IEEE Trans. Fuzzy Syst., 25 (2016), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005 doi: 10.1109/TFUZZ.2016.2604005
    [41] R. R. Yager, N. Alajlan, Y. Bazi, Aspects of generalized orthopair fuzzy sets, Int. J. Intell. Syst., 33 (2018), 2154–2174. https://doi.org/10.1002/int.22008 doi: 10.1002/int.22008
    [42] C. Yu, Y. Shao, K. Wang, L. Zhang, A group decision making sustainable supplier selection approach using extended TOPSIS under interval-valued Pythagorean fuzzy environment, Expert Syst. Appl., 121 (2019), 1–17. https://doi.org/10.1016/j.eswa.2018.12.010 doi: 10.1016/j.eswa.2018.12.010
    [43] W. Yang, Y. Pang, New q-rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making, Int. J. Intell. Syst., 34 (2019), 439–476. https://doi.org/10.1002/int.22060 doi: 10.1002/int.22060
    [44] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353. https://doi.org/10.2307/2272014 doi: 10.2307/2272014
    [45] X. Zhang, Z. Xu, Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, Int. J. Intell. Syst., 29 (2014), 1061–1078. https://doi.org/10.1002/int.21676 doi: 10.1002/int.21676
    [46] Z. Zhang, C. Guo, Consistency-based algorithms to estimate missing elements for uncertain 2-tuple linguistic preference relations, Int. J. Comput. Intell. Syst., 7 (2014), 924–936. https://doi.org/10.1080/18756891.2013.856254 doi: 10.1080/18756891.2013.856254
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