Volume 8, Issue 2, April 2015, Pages 226 - 239
A note on operations of hesitant fuzzy sets
Zheng Pei, Liangzhong Yi
Received 22 March 2014, Accepted 20 September 2014, Available Online 1 April 2015.
- https://doi.org/10.1080/18756891.2015.1001947How to use a DOI?
- hesitant fuzzy sets, operations, the lattice, the residuated lattice
- In this paper, properties of operations and algebraic structures of hesitant fuzzy sets are investigated. Semilattices of hesitant fuzzy sets with union and intersection are discussed, respectively. By using ⊕ and ⊗ operators, the commutative monoid of hesitant fuzzy sets is provided, moreover, the lattice and distributive lattice of hesitant fuzzy sets are defined on the equivalence class of hesitant fuzzy sets. Based on the distributive lattice of hesitant fuzzy sets, the residuated lattices of hesitant fuzzy sets are constructed by residual implications, which are induced by intersection and ⊗, respectively. From the theoretical point of view, algebraic structures of hesitant fuzzy sets are useful for approximate reasoning and decision making to deal with hesitancy of information.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - Zheng Pei AU - Liangzhong Yi PY - 2015 DA - 2015/04/01 TI - A note on operations of hesitant fuzzy sets JO - International Journal of Computational Intelligence Systems SP - 226 EP - 239 VL - 8 IS - 2 SN - 1875-6883 UR - https://doi.org/10.1080/18756891.2015.1001947 DO - https://doi.org/10.1080/18756891.2015.1001947 ID - Pei2015 ER -