International Journal of Computational Intelligence Systems

Volume 8, Issue 2, April 2015, Pages 226 - 239

A note on operations of hesitant fuzzy sets

Authors
Zheng Pei, Liangzhong Yi
Corresponding Author
Zheng Pei
Received 22 March 2014, Accepted 20 September 2014, Available Online 1 April 2015.
DOI
https://doi.org/10.1080/18756891.2015.1001947How to use a DOI?
Keywords
hesitant fuzzy sets, operations, the lattice, the residuated lattice
Abstract
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.

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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
8 - 2
Pages
226 - 239
Publication Date
2015/04/01
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
https://doi.org/10.1080/18756891.2015.1001947How to use a DOI?
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  -