IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i12p280-d185417.html
   My bibliography  Save this article

Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators with New Distance Measures

Author

Listed:
  • Harish Garg

    (School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University) Patiala, Punjab 147004, India)

  • Gagandeep Kaur

    (School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University) Patiala, Punjab 147004, India)

Abstract

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

Suggested Citation

  • Harish Garg & Gagandeep Kaur, 2018. "Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators with New Distance Measures," Mathematics, MDPI, vol. 6(12), pages 1-30, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:280-:d:185417
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/12/280/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/6/12/280/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bin Zhu & Zeshui Xu & Meimei Xia, 2012. "Dual Hesitant Fuzzy Sets," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, May.
    2. Dheeraj Kumar Joshi & Ismat Beg & Sanjay Kumar, 2018. "Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems," Mathematics, MDPI, vol. 6(4), pages 1-20, March.
    3. Zeshui Xu & Wei Zhou, 2017. "Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment," Fuzzy Optimization and Decision Making, Springer, vol. 16(4), pages 481-503, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhen-Song Chen & Min Li & Wen-Tao Kong & Kwai-Sang Chin, 2019. "Evaluation and Selection of HazMat Transportation Alternatives: A PHFLTS- and TOPSIS-Integrated Multi-Perspective Approach," IJERPH, MDPI, vol. 16(21), pages 1-33, October.
    2. Aleksandra Łapko & Ewa Hącia & Roma Strulak-Wójcikiewicz & Kevser Çınar & Enrico Panai & Lovorko Lučić, 2021. "Eco-Friendly Tourism Decision Making during COVID-19—Sailing Tourism Example," Sustainability, MDPI, vol. 14(1), pages 1-15, December.

    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. Dheeraj Kumar Joshi & Ismat Beg & Sanjay Kumar, 2018. "Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems," Mathematics, MDPI, vol. 6(4), pages 1-20, March.
    2. Qasim Noor & Tabasam Rashid & Syed Muhammad Husnine, 2021. "An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-24, May.
    3. Huiping Chen & Guiqiong Xu & Pingle Yang, 2019. "Multi-Attribute Decision-Making Approach Based on Dual Hesitant Fuzzy Information Measures and Their Applications," Mathematics, MDPI, vol. 7(9), pages 1-18, August.
    4. Hüseyin Akay & Müsteyde Baduna Koçyiğit, 2021. "An Approach for Determination of the Drainage Network Effect on GIUH Using Hesitant Probabilistic Fuzzy Linguistic Sets," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(11), pages 3873-3902, September.
    5. Hongyue Diao & Ansheng Deng & Hui Cui & Xin Liu & Li Zou, 2022. "An approach for solving fuzzy multi-criteria decision problem under linguistic information," Fuzzy Optimization and Decision Making, Springer, vol. 21(1), pages 45-69, March.
    6. Chaube, Shshank & Joshi, Dheeraj Kumar & Ujarari, Chandan Singh, 2023. "Hesitant Bifuzzy Set (an introduction): A new approach to assess the reliability of the systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 98-107.
    7. Hui Gao & Linggang Ran & Guiwu Wei & Cun Wei & Jiang Wu, 2020. "VIKOR Method for MAGDM Based on Q-Rung Interval-Valued Orthopair Fuzzy Information and Its Application to Supplier Selection of Medical Consumption Products," IJERPH, MDPI, vol. 17(2), pages 1-14, January.
    8. Xiao-kang Wang & Sheng-hui Wang & Hong-yu Zhang & Jian-qiang Wang & Lin Li, 2021. "The Recommendation Method for Hotel Selection Under Traveller Preference Characteristics: A Cloud-Based Multi-Criteria Group Decision Support Model," Group Decision and Negotiation, Springer, vol. 30(6), pages 1433-1469, December.
    9. Li Li & Hegong Lei & Jun Wang, 2020. "Q -Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making," Mathematics, MDPI, vol. 8(9), pages 1-34, September.
    10. Asma Mahmood & Mohsan Raza, 2021. "Observation of a Change in Human Attitude in a Decision Making Process Equipped with an Interference of a Third Party," Mathematics, MDPI, vol. 9(21), pages 1-14, November.
    11. Sarka Hoskova-Mayerova & Madeline Al Tahan & Bijan Davvaz, 2020. "Fuzzy Multi-Hypergroups," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    12. Mei Tang & Jie Wang & Jianping Lu & Guiwu Wei & Cun Wei & Yu Wei, 2019. "Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making," Mathematics, MDPI, vol. 7(4), pages 1-27, April.
    13. Wang Feng, 2019. "Aggregation Similarity Measure Based on Hesitant Fuzzy Closeness Degree and Its Application to Clustering Analysis," Journal of Systems Science and Information, De Gruyter, vol. 7(1), pages 70-89, February.
    14. Saleem Abdullah & Alaa O. Almagrabi & Ihsan Ullah, 2023. "A New Approach to Artificial Intelligent Based Three-Way Decision Making and Analyzing S-Box Image Encryption Using TOPSIS Method," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    15. Songtao Shao & Xiaohong Zhang, 2019. "Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes," Mathematics, MDPI, vol. 7(7), pages 1-23, July.
    16. Pavle Milošević & Bratislav Petrović & Ivana Dragović, 2021. "A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra," Mathematics, MDPI, vol. 9(17), pages 1-21, September.
    17. Weiming Li & Jun Ye, 2022. "Group Decision-Making Problems Based on Mixed Aggregation Operations of Interval-Valued Fuzzy and Entropy Elements in Single- and Interval-Valued Fuzzy Environments," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    18. M. G. Brikaa & Zhoushun Zheng & El-Saeed Ammar, 2020. "Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals," Mathematics, MDPI, vol. 8(3), pages 1-30, February.
    19. Kumar, Sourabh & Barua, Mukesh Kumar, 2023. "Exploring the hyperledger blockchain technology disruption and barriers of blockchain adoption in petroleum supply chain," Resources Policy, Elsevier, vol. 81(C).
    20. Fanyong Meng & Aiqing Zeng & Jie Tang & Witold Pedrycz, 2023. "Ranking Objects from Individual Linguistic Dual Hesitant Fuzzy Information in View of Optimal Model-Based Consistency and Consensus Iteration Algorithm," Group Decision and Negotiation, Springer, vol. 32(1), pages 5-44, February.

    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:gam:jmathe:v:6:y:2018:i:12:p:280-:d:185417. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.