A note on operations of hesitant fuzzy sets

DOI

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.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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  - 10.1080/18756891.2015.1001947
ID  - Pei2015
ER  -