Search Advanced

AIMS Mathematics

2024, Volume 9, Issue 12: 35860-35884. doi: 10.3934/math.20241700
Previous Article Next Article
Research article

Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information

  • 1.
    Department of Mathematics, Faculty of Basic and Applied Sciences, Air University PAF Complex E-9, Islamabad, 44000, Pakistan
  • 2.
    Department of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, Punjab, India
  • 3.
    Department of Physics, Faculty of Basic and Applied Sciences, Air University PAF Complex E-9, Islamabad, 44000, Pakistan
  • 4.
    Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
  • Received: 05 September 2024 Revised: 18 November 2024 Accepted: 03 December 2024 Published: 24 December 2024

  • MSC : 03B52, 03E72, 90B50

  • The Choquet integral is a fuzzy measure that serves as an effective aggregation operator for combining a limited number of components into a single set. In 1978, Hamacher introduced the Hamacher t-norm and t-conorm, an expanded version of algebraic t-norms. In this article, we present the aggregation operators for the Choquet integral that utilize the Hamacher t-norms to handle the theory of complex intuitionistic fuzzy values. These operators include the complex intuitionistic fuzzy Hamacher Choquet integral averaging and geometric operators. Additionally, an analysis is conducted on the attributes and special situations of the suggested methodologies. In addition, a novel approach is presented, utilizing newly developed operators for solving multi-attribute decision-making issues with complex intuitionistic fuzzy values. The operational stages of this strategy are thoroughly presented. Finally, we conducted a comprehensive comparison between the proposed methodology and existing approaches, using illustrative examples to validate the effectiveness and demonstrate the advantages of the proposed methods.

    Citation: Tehreem, Harish Garg, Kinza Ayaz, Walid Emam. Multi attribute decision-making algorithms using Hamacher Choquet-integral operators with complex intuitionistic fuzzy information[J]. AIMS Mathematics, 2024, 9(12): 35860-35884. doi: 10.3934/math.20241700

    Related Papers:

  • The Choquet integral is a fuzzy measure that serves as an effective aggregation operator for combining a limited number of components into a single set. In 1978, Hamacher introduced the Hamacher t-norm and t-conorm, an expanded version of algebraic t-norms. In this article, we present the aggregation operators for the Choquet integral that utilize the Hamacher t-norms to handle the theory of complex intuitionistic fuzzy values. These operators include the complex intuitionistic fuzzy Hamacher Choquet integral averaging and geometric operators. Additionally, an analysis is conducted on the attributes and special situations of the suggested methodologies. In addition, a novel approach is presented, utilizing newly developed operators for solving multi-attribute decision-making issues with complex intuitionistic fuzzy values. The operational stages of this strategy are thoroughly presented. Finally, we conducted a comprehensive comparison between the proposed methodology and existing approaches, using illustrative examples to validate the effectiveness and demonstrate the advantages of the proposed methods.



    加载中


    [1] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0898-1221(05)80044-1 doi: 10.1016/S0898-1221(05)80044-1
    [2] H. Wang, S. Kwong, Y. Jin, W. Wei, K. F. Man, Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction, Fuzzy Set. Syst., 149 (2005), 149–186. https://doi.org/10.1016/j.fss.2004.07.002 doi: 10.1016/j.fss.2004.07.002
    [3] Y. Chalco-Cano, H. Román-Flores, Comparison between some approaches to solve fuzzy differential equations, Fuzzy Set. Syst., 160 (2009), 1517–1527. https://doi.org/10.1016/j.fss.2008.12.013 doi: 10.1016/j.fss.2008.12.013
    [4] M. Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Appl. Math. Comput., 179 (2006), 328–343. https://doi.org/10.1016/j.amc.2005.11.151 doi: 10.1016/j.amc.2005.11.151
    [5] W. Heiden, J. Brickmann, Segmentation of protein surfaces using fuzzy logic, J. Mol. Graph., 12 (1994), 106–115. https://doi.org/10.1016/0263-7855(94)80008-2 doi: 10.1016/0263-7855(94)80008-2
    [6] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst. 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
    [7] J. Liu, J. Mai, H. Li, B. Huang, Y. Liu, On three perspectives for deriving three-way decision with linguistic intuitionistic fuzzy information, Inform. Sciences, 588 (2022), 350–380. https://doi.org/10.1016/j.ins.2021.12.066 doi: 10.1016/j.ins.2021.12.066
    [8] D. Xie, F. Xiao, W. Pedrycz, Information quality for intuitionistic fuzzy values with its application in decision making, Eng. Appl. Artif. Intel., 109 (2022), 104568. https://doi.org/10.1016/j.engappai.2021.104568 doi: 10.1016/j.engappai.2021.104568
    [9] Y. Liu, G. Wei, H. Liu, L. Xu, Group decision making for internet public opinion emergency based upon linguistic intuitionistic fuzzy information, Int. J. Mach. Learn. Cyb., 13 (2022), 579–594. https://doi.org/10.1007/s13042-021-01368-2 doi: 10.1007/s13042-021-01368-2
    [10] H. Garg, G. Kaur, Algorithm for solving the decision-making problems based on correlation coefficients under cubic intuitionistic fuzzy information: a case study in watershed hydrological system, Complex Intell. Syst., 8 (2022), 179–198. https://doi.org/10.1007/s40747-021-00440-5 doi: 10.1007/s40747-021-00440-5
    [11] W. Wang, J. Zhan, J. Mi, A three-way decision approach with probabilistic dominance relations under intuitionistic fuzzy information, Inform. Sciences, 582 (2022), 114–145. https://doi.org/10.1016/j.ins.2021.11.084 doi: 10.1016/j.ins.2021.11.084
    [12] F. Ecer, An extended MAIRCA method using intuitionistic fuzzy sets for coronavirus vaccine selection in the age of COVID-19, Neural Comput. Appl., 34 (2022), 5603–5623. https://doi.org/10.1007/s00521-021-06276-y doi: 10.1007/s00521-021-06276-y
    [13] H. Zhang, X. Zuo, B. Sun, B. Wei, J. Fu, X. Xiao, Fuzzy-PID-based atmosphere packaging gas distribution system for fresh food, Appl. Sciences, 13 (2023), 2674. https://doi.org/10.3390/app13042674 doi: 10.3390/app13042674
    [14] H. Garg, Z. Ali, T. Mahmood, M. R. Ali, A. Alburaikan, Schweizer-Sklar prioritized aggregation operators for intuitionistic fuzzy information and their application in multi-attribute decision-making, Alex. Eng. J., 67 (2023), 229–240. https://doi.org/10.1016/j.aej.2022.04.030 doi: 10.1016/j.aej.2022.04.030
    [15] T. Mahmood, W. Ali, Z. Ali, R. Chinram, Power aggregation operators and similarity measures based on improved intuitionistic hesitant fuzzy sets and their applications to multiple attribute decision making, CMES-Comp. Model. Eng., 126 (2021), 1165–1187. https://doi.org/10.32604/cmes.2021.015634 doi: 10.32604/cmes.2021.015634
    [16] D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex fuzzy sets, IEEE T. Fuzzy Syst., 10 (2002), 171–186. https://doi.org/10.1109/91.995119 doi: 10.1109/91.995119
    [17] 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. https://doi.org/10.3233/JIFS-191712 doi: 10.3233/JIFS-191712
    [18] 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.2021.3078248 doi: 10.1109/ACCESS.2021.3078248
    [19] A. M. D. Alkouri, A. R. Salleh, Complex intuitionistic fuzzy sets, AIP Conference Proceedings, 1482 (2012), 464–470. https://doi.org/10.1063/1.4757475
    [20] T. Mahmood, Z. Ali, Multi-attribute decision-making methods based on Aczel–Alsina power aggregation operators for managing complex intuitionistic fuzzy sets, Comput. Appl. Math., 42 (2023), 1–34. https://doi.org/10.1007/s40314-022-02116-1 doi: 10.1007/s40314-022-02116-1
    [21] D. Rani, H. Garg, Multiple attributes group decision-making based on trigonometric operators, particle swarm optimization and complex intuitionistic fuzzy values, Artif. Intell. Rev., 56 (2023), 1787–1831. https://doi.org/10.1007/s10462-022-10236-8 doi: 10.1007/s10462-022-10236-8
    [22] W. Azeem, W. Mahmood, T. Mahmood, Z. Ali, M. Naeem, Analysis of Einstein aggregation operators based on complex intuitionistic fuzzy sets and their applications in multi-attribute decision-making, AIMS Math., 8 (2023), 6036–6063. https://doi.org/10.3934/math.2023366 doi: 10.3934/math.2023366
    [23] 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/s12559-019-09680-0 doi: 10.1007/s12559-019-09680-0
    [24] Z. Ali, T. Mahmood, M. Aslam, R. Chinram, Another view of complex intuitionistic fuzzy soft sets based on prioritized aggregation operators and their applications to multiattribute decision making, Mathematics, 9 (2021), 1922. https://doi.org/10.3390/math9161922 doi: 10.3390/math9161922
    [25] H. Hamacher, Über Logische Verknüpfungen Unscharfer Aussagen und deren Zugehörige Bewertungsfunktionen, Working Paper No. 75/14, Lehrstuhl für Unternehmensforschung, RWTH Aachen University, 1975.
    [26] G. Choquet, Theory of capacities, Ann. I. Fourier, 5 (1953), 131–295. https://doi.org/10.5802/aif.53 doi: 10.5802/aif.53
    [27] J. Y. Huang, Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, J. Intell. Fuzzy Syst., 27 (2014), 505–513. https://doi.org/10.3233/IFS-130810 doi: 10.3233/IFS-130810
    [28] M. Akram, X. Peng, A. Sattar, A new decision-making model using complex intuitionistic fuzzy Hamacher aggregation operators, Soft Comput., 25 (2021), 7059–7086. https://doi.org/10.1007/s00500-021-05737-w doi: 10.1007/s00500-021-05737-w
    [29] Z. Xu, Choquet integrals of weighted intuitionistic fuzzy information, Inform. Sciences, 180 (2010), 726–736. https://doi.org/10.1016/j.ins.2009.11.033 doi: 10.1016/j.ins.2009.11.033
    [30] X. Jia, Y. Wang, Choquet integral-based intuitionistic fuzzy arithmetic aggregation operators in multi-criteria decision-making, Expert Syst. Appl., 191 (2022), 116242. https://doi.org/10.1016/j.eswa.2021.116242 doi: 10.1016/j.eswa.2021.116242
    [31] C. Tan, X. Chen, Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making, Expert Syst. Appl., 37 (2010), 149–157. https://doi.org/10.1016/j.eswa.2009.05.065 doi: 10.1016/j.eswa.2009.05.065
    [32] C. Tan, X. Chen, Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making, Int. J. Intell. Syst., 26 (2011), 659–686. https://doi.org/10.1002/int.20474 doi: 10.1002/int.20474
    [33] T. Mahmood, Z. Ali, S. Baupradist, R. Chinram, TOPSIS method based on Hamacher Choquet-integral aggregation operators for Atanassov-intuitionistic fuzzy sets and their applications in decision-making, Axioms, 11 (2022), 715. https://doi.org/10.3390/axioms11120715 doi: 10.3390/axioms11120715
    [34] T. Mahmood, Z. Ali, S. Baupradist, R. Chinram, Complex intuitionistic fuzzy Aczel-Alsina aggregation operators and their application in multi-attribute decision-making, Symmetry, 14 (2022), 2255. https://doi.org/10.3390/sym14112255 doi: 10.3390/sym14112255
    [35] P. A. Ejegwa, S. Ahemen, Enhanced intuitionistic fuzzy similarity operators with applications in emergency management and pattern recognition, Granular Comput., 8 (2023), 361–372. https://doi.org/10.1007/s41066-022-00323-3 doi: 10.1007/s41066-022-00323-3
    [36] M. Akram, M. Khan, R. Ali, A new decision-making model using complex intuitionistic fuzzy Hamacher aggregation operators, Springer, 2023. https://doi.org/10.1007/978-3-030-71571-6
    [37] A. A. Q. Al-Qubati, L. Zedam, K. Ullah, H. F. Al-Qahtani, Choquet-integral aggregation operators based on Hamacher t-norm and t-conorm for complex intuitionistic fuzzy TOPSIS technique to deal with socio-economic problems, IEEE Access, 12 (2023), 3098–3113. https://doi.org/10.1109/ACCESS.2023.3346499 doi: 10.1109/ACCESS.2023.3346499
    [38] H. M. Talib, A. S. Albahri, T. O. C. Edoh, Fuzzy decision-making framework for sensitively prioritizing autism patients with moderate emergency level, Appl. Data Sci. Anal., 2023 (2023), 16–41. https://doi.org/10.1016/j.ads2023.2023.001 doi: 10.1016/j.ads2023.2023.001
    [39] S. Mohammed, A. K. Oleiwi, T. K. Asman, H. M. Saleh, A. M. Mahmood, I. Avci, A survey of MCDM-based software engineering method, Babylonian J. Math., 2024 (2024), 13–18. https://doi.org/10.1234/bjm2024.01318 doi: 10.1234/bjm2024.01318
    [40] D. David, A. Alamoodi, A bibliometric analysis of research on multiple criteria decision making with emphasis on energy sector between 2019–2023, Appl. Data Sci. Anal., 2023 (2023), 143–149. https://doi.org/10.1016/j.ads2023.2023.0149 doi: 10.1016/j.ads2023.2023.0149
    [41] M. Aljanabi, Navigating the Landscape: A comprehensive bibliometric analysis of decision-making research in civil engineering, Mesopotamian J. Civil Eng., 2023 (2023) https://doi.org/10.58496/MJCE/2023/005
    [42] L. Jing, X. Fan, D. Feng, C. Lu, S. Jiang, A patent text-based product conceptual design decision-making approach considering the fusion of incomplete evaluation semantic and scheme beliefs, Appl. Soft Comput., 157 (2024), 111492. https://doi.org/10.1016/j.asoc.2024.111492 doi: 10.1016/j.asoc.2024.111492
    [43] C. Zhu, An adaptive agent decision model based on deep reinforcement learning and autonomous learning, J. Log., Inform. Serv. Sci., 10 (2023), 107–118. https://doi.org/10.33168/JLISS.2023.0309 doi: 10.33168/JLISS.2023.0309
  • Reader Comments
  • © 2024 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
AIMS Mathematics
1.8 3.4

Metrics

Article views(189) PDF downloads(18) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(9)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog