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Dual Hesitant Fuzzy Sets

Author

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  • Bin Zhu
  • Zeshui Xu
  • Meimei Xia

Abstract

In recent decades, several types of sets, such as fuzzy sets, interval‐valued fuzzy sets, intuitionistic fuzzy sets, interval‐valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, use a notion of nested interval to reflect their common ground, then propose an extension principle of DHFSs. Additionally, we give an example to illustrate the application of DHFSs in group forecasting.

Suggested Citation

  • Bin Zhu & Zeshui Xu & Meimei Xia, 2012. "Dual Hesitant Fuzzy Sets," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:879629
    DOI: 10.1155/2012/879629
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    Cited by:

    1. Rohit & Kamal Kumar & Reeta Bhardwaj & Gagandeep Kaur, 2025. "Rainfall Analysis using FUCOM Weighted Logarithmic Distance Measure Based on Probabilistic Dual Hesitant Preference Values," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 39(1), pages 207-226, January.
    2. Yanbing Ju & Shanghong Yang & Xiaoyue Liu, 2014. "A Novel Method for Multiattribute Decision Making with Dual Hesitant Fuzzy Triangular Linguistic Information," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Xun Zhang & Jun Wang, 2023. "Q‐Rung Interval‐Valued Probabilistic Dual Hesitant Fuzzy Sets: A New Tool for Multiattribute Group Decision‐Making," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    4. Lei Wang & Mingfang Ni & Lei Zhu, 2013. "Correlation Measures of Dual Hesitant Fuzzy Sets," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Huimin Zhang, 2014. "Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    6. Zhi-Hui Li, 2014. "An Extension of the MULTIMOORA Method for Multiple Criteria Group Decision Making Based upon Hesitant Fuzzy Sets," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    7. Soniya Gupta & Dheeraj Kumar Joshi, 2025. "Series of novel score functions for Hesitant Bifuzzy set and its application in transportation problem," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 16(8), pages 2785-2799, August.
    8. Chunyong Wang & Qingguo Li & Xiaoqiang Zhou, 2014. "Multiple Attribute Decision Making Based on Generalized Aggregation Operators under Dual Hesitant Fuzzy Environment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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