The notion of a hesitant fuzzy semigroup with a frontier is introduced, and several properties are investigated. Characterizations of a hesitant fuzzy semigroup with a frontier are considered, and a condition for a special set to be a subsemigroup is provided. The hesitant union and hesitant intersection of two hesitant fuzzy semigroups with a frontier are dealt with, and the hesitant fuzzy pre-image and hesitant fuzzy image of a hesitant fuzzy semigroup with a frontier under the homomorphism are discussed.
JunY.B., KhanA. and SongS.Z., Hesitant fuzzy interior ideals in semigroups, Bull Iranian Math Soc(submitted).
2.
JunY.B. and KhanM., Hesitant fuzzy ideals in semigroups, J Intell Fuzzy Systems(submitted).
3.
JunY.B. and SongS.Z., Hesitant fuzzy set theory applied to filters in MTL-algebras, Honam Math J36(4) (2014), 813–830.
4.
JunY.B. and SongS.Z., Hesitant fuzzy prefilters and filters of EQ-algebras, Appl Math Sci9 (2015), 515–532.
5.
LiaoH., XuZ. and ZengX.J., Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making, Inform Sci271 (2014), 125–142.
6.
RodriguezR.M., MartinezL. and HerreraF., Hesitant fuzzy linguistic term sets for decision making, IEEE Trans Fuzzy Syst20(1) (2012), 109–119.
7.
TorraV., Hesitant fuzzy sets, Int J Intell Syst25 (2010), 529–539.
8.
TorraV. and NarukawaY., On hesitant fuzzy sets and decision, in: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, pp. 1378–1382.
9.
WeiG., Hesitant fuzzy prioritized operators and their application to multiple attribute decision making, Knowledge-Based Systems31 (2012), 176–182.
10.
XiaM. and XuZ.S., Hesitant fuzzy information aggregation in decision making, Internat J Approx Reason52(3) (2011), 395–407.
11.
XiaM., XuZ.S. and ChenN., Some hesitant fuzzy aggregation operators with their application in group decision making, Group Decision Negotiation22 (2013), 259–279.
12.
XuZ.S. and XiaM., Distance and similarity measures for hesitant fuzzy sets, Inform Sci181(11) (2011), 2128–2138.
