IDEAS home Printed from https://ideas.repec.org/a/wly/jnlmpe/v2023y2023i1n3516707.html

Generalized Heronian Mean Operators Based on Archimedean T‐Norms of the Complex Picture Fuzzy Information and Their Application to Decision‐Making

Author

Listed:
  • Harish Garg
  • Zeeshan Ali
  • Jeonghwan Gwak
  • Ibrahim M. Hezam

Abstract

Complex picture fuzzy set is a special picture fuzzy set where the truth, abstinence, and falsity grades are shown by a complex number and can effortlessly illustrate the problem and inconsistency in the genuine world. T‐norm and t‐conorm play an essential and beneficial role in the environment of fuzzy set theory; similarly, Archimedean t‐norm and t‐conorm have massive flexibility and dominancy in the information fusion procedure. The major contribution of this analysis is to explore the algebraic, Einstein, Hamacher, and Frank operational laws under the complex picture fuzzy set. Moreover, the principle of complex picture fuzzy Archimedean Heronian aggregation operator and complex picture fuzzy weighted Archimedean Heronian aggregation operator are also elaborated by using Archimedean t‐norm and t‐conorm. Additionally, by using the elaborated operators, a multiattribute decision‐making technique is presented to elaborate the consistency and reliability of the explored works. Finally, many examples are illustrated for discussing the advantages and sensitive analysis and graphical representation of the investigated works.

Suggested Citation

  • Harish Garg & Zeeshan Ali & Jeonghwan Gwak & Ibrahim M. Hezam, 2023. "Generalized Heronian Mean Operators Based on Archimedean T‐Norms of the Complex Picture Fuzzy Information and Their Application to Decision‐Making," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:3516707
    DOI: 10.1155/2023/3516707
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2023/3516707
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/3516707?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Songsong Dai & Lvqing Bi & Bo Hu, 2019. "Distance Measures between the Interval-Valued Complex Fuzzy Sets," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    2. Harish Garg & R. Sujatha & D. Nagarajan & J. Kavikumar & Jeonghwan Gwak & Sami Ullah Khan, 2021. "Evidence Theory in Picture Fuzzy Set Environment," Journal of Mathematics, Hindawi, vol. 2021, pages 1-8, May.
    3. Liangping Wu & Guiwu Wei & Jiang Wu & Cun Wei, 2020. "Some Interval-Valued Intuitionistic Fuzzy Dombi Heronian Mean Operators and their Application for Evaluating the Ecological Value of Forest Ecological Tourism Demonstration Areas," IJERPH, MDPI, vol. 17(3), pages 1-31, January.
    4. Pratiksha Tiwari, 2021. "Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making," International Journal of Fuzzy System Applications (IJFSA), IGI Global Scientific Publishing, vol. 10(1), pages 64-93, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuqi Zang & Jiamei Zhao & Wenchao Jiang & Tong Zhao, 2024. "Advanced Linguistic Complex T-Spherical Fuzzy Dombi-Weighted Power-Partitioned Heronian Mean Operator and Its Application for Emergency Information Quality Assessment," Sustainability, MDPI, vol. 16(7), pages 1-35, April.
    2. Asima Razzaque & Ibtisam Masmali & Rimsha Hassan & Umer Shuaib & Abdul Razaq & Ghaliah Alhamzi & Saima Noor, 2023. "A Modern Strategy for the Selection of Efficacious Solar Panels at Industrial Level under an Interval-Valued Picture Fuzzy Set Hybrid Environment," Energies, MDPI, vol. 16(14), pages 1-22, July.
    3. Tahir Mahmood & Ubaid ur Rehman & Zeeshan Ali & Muhammad Aslam & Ronnason Chinram, 2022. "Identification and Classification of Aggregation Operators Using Bipolar Complex Fuzzy Settings and Their Application in Decision Support Systems," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    4. Jianping Lu & Tingting He & Guiwu Wei & Jiang Wu & Cun Wei, 2020. "Cumulative Prospect Theory: Performance Evaluation of Government Purchases of Home-Based Elderly-Care Services Using the Pythagorean 2-tuple Linguistic TODIM Method," IJERPH, MDPI, vol. 17(6), pages 1-21, March.
    5. Lihua Liu & Jing Huang & Huimin Wang, 2020. "Visibility Graph Power Geometric Aggregation Operator and Its Application in Water, Energy and Food Efficiency Evaluation," IJERPH, MDPI, vol. 17(11), pages 1-16, May.
    6. Shahzaib Ashraf & Razia Choudhary & Muhammad Sohail & Gokul K. C., 2025. "Optimizing Business Investments Using a Novel Approach Based on Picture Hesitant Fuzzy Soft Aggregation Information," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    7. Tran Manh Tuan & Luong Thi Hong Lan & Shuo-Yan Chou & Tran Thi Ngan & Le Hoang Son & Nguyen Long Giang & Mumtaz Ali, 2020. "M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing," Mathematics, MDPI, vol. 8(5), pages 1-24, May.
    8. Li Wang & Myagmarsuren Damdinsuren & Yuanhao Qin & Ganzorig Gonchigsumlaa & Yadmaa Zandan & Zilin Zhang, 2024. "Forest Wellness Tourism Development Strategies Using SWOT, QSPM, and AHP: A Case Study of Chongqing Tea Mountain and Bamboo Forest in China," Sustainability, MDPI, vol. 16(9), pages 1-25, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:3516707. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/2629 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.