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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 ð ‘› 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, Hindawi, vol. 2012, pages 1-13, May.
    • Handle: RePEc:hin:jnljam:879629
    DOI: 10.1155/2012/879629
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    Cited by:

    1. 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.
    2. 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).
    3. Xiaonan Ji & Lixia Yu & Jiapei Fu, 2019. "Evaluating Personal Default Risk in P2P Lending Platform: Based on Dual Hesitant Pythagorean Fuzzy TODIM Approach," Mathematics, MDPI, vol. 8(1), pages 1-14, December.
    4. 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.
    5. 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.
    6. Xiaowen Qi & Junling Zhang & Changyong Liang, 2018. "Multiple Attributes Group Decision-Making Approaches Based on Interval-Valued Dual Hesitant Fuzzy Unbalanced Linguistic Set and Their Applications," Complexity, Hindawi, vol. 2018, pages 1-22, April.
    7. 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.
    8. 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.
    9. Chachra, Aayushi & Kumar, Akshay & Ram, Mangey, 2023. "Intuitionistic fuzzy approach to reliability assessment of multi-state systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 489-503.
    10. 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.
    11. Yan Ni & Hua Zhao & Zeshui Xu & Zeyan Wang, 2022. "Multiple attribute decision-making method based on projection model for dual hesitant fuzzy set," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 263-289, June.
    12. Xiaotong Qie & Rui Zhang & Yanyong Hu & Xialing Sun & Xue Chen, 2021. "A Multi-Criteria Decision-Making Approach for Energy Storage Technology Selection Based on Demand," Energies, MDPI, vol. 14(20), pages 1-29, October.
    13. Kumar, Sourabh, 2023. "Evaluation and analysis of India's energy security: A policy perspective," Energy, Elsevier, vol. 278(PB).
    14. Guohua Qu & Rudan Xue & Tianjiao Li & Weihua Qu & Zeshui Xu, 2020. "A Stochastic Multi-Attribute Method for Measuring Sustainability Performance of a Supplier Based on a Triple Bottom Line Approach in a Dual Hesitant Fuzzy Linguistic Environment," IJERPH, MDPI, vol. 17(6), pages 1-26, March.
    15. 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.
    16. Junling Zhang & Linying Shen & Lijun Liu & Xiaowen Qi & Changyong Liang, 2022. "Tackling Comprehensive Evaluation of Tourism Community Resilience: A Probabilistic Hesitant Linguistic Group Decision Making Approach," Land, MDPI, vol. 11(10), pages 1-32, September.
    17. Xiao-Wen Qi & Jun-Ling Zhang & Shu-Ping Zhao & Chang-Yong Liang, 2017. "Tackling Complex Emergency Response Solutions Evaluation Problems in Sustainable Development by Fuzzy Group Decision Making Approaches with Considering Decision Hesitancy and Prioritization among Asse," IJERPH, MDPI, vol. 14(10), pages 1-35, October.
    18. 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.
    19. Zhenghai Ai & Xiaoqin Shu & Zeshui Xu, 2019. "Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data," Complexity, Hindawi, vol. 2019, pages 1-14, October.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.

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