Dual Hesitant Fuzzy Sets
By Bin Zhu, Zeshui Xu, Meimei Xia. Journal of Applied Mathematics, 2012
665 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/d38ce296612a1707aac9a7c5968154a35f25a8b0
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Zeshui Xu
- Huchang Liao
- Francisco Herrera
- Rosa M. Rodríguez
- Luis Martínez-López
- Bahram Farhadinia
- Enrique Herrera-Viedma
- Vicenç Torra
In Computational Theory and Mathematics
- Zeshui Xu
- Huchang Liao
- Francisco Herrera
- Luis Martínez-López
- Rosa M. Rodríguez
- Enrique Herrera-Viedma
- Bahram Farhadinia
- Xiao-Jun Zeng
In Management Science and Operations Research
- Zeshui Xu
- Huchang Liao
- Francisco Herrera
- Luis Martínez-López
- Rosa M. Rodríguez
- Bahram Farhadinia
- Enrique Herrera-Viedma
- Xiao-Jun Zeng
Citations in the corpus
- A VIKOR-based method for hesitant fuzzy multi-criteria decision making (2013, methodology): “Additionally, Zhu et al. (2012b) investigated the hesitant fuzzy geometric Bonferroni means and applied them to multi-criteria linguistic decision making.”
- Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets (2013, background): “Later, a number of other extensions of the HFSs have been developed such as dual hesitant fuzzy sets (DHFSs) [43], generalized hesitant fuzzy sets (GHFSs) [16] and hesitant fuzzy linguistic term sets (HFLTSs) [17].”
- Hesitant Fuzzy Sets: State of the Art and Future Directions (2014, background): “15 Furthermore, a practical example of group forecasting was shown.”