We introduce the notions of ε-hesitant fuzzy ideal, ε-hesitant fuzzy bi-ideal and ε-hesitant fuzzy interior ideal on semigroup and characterizations of a hesitant fuzzy ideal(bi-ideal, interior ideal) with a frontier are considered and provide a condition for a special set to be an ideal. We provide an example to show that ε-hesitant fuzzy ideal on semigroup may not be hesitant fuzzy ideal. Moreover, we show that the hesitant intersection of two hesitant fuzzy left (right, bi-, interior) ideal with frontier is a hesitant fuzzy left(right, bi-, interior) ideal respectively with frontier.
ε-hesitant fuzzy semigroup, ε-hesitant fuzzy ideal
