AbstractIn this paper, the notions of hesitant anti-intuitionistic fuzzy soft BCI-commutative ideals of BCI-algebras and hesitant anti intuitionistic fuzzy soft sub commutative ideals of BCK-algebras are introduced and their related properties are investigate. Relations between a hesitant anti intuitionistic fuzzy soft ideals and hesitant anti intuitionistic fuzzy soft BCI-commutative ideals are discussed. Conditions for a hesitant anti-intuitionistic fuzzy soft ideal to be a hesitant anti intuitionistic fuzzy soft BCI commutative ideal are provided. Finally, it is proved that a hesitant anti-intuitionistic fuzzy soft p-ideal is a hesitant anti-intuitionistic fuzzy soft sub commutative ideal in a BCK algebra.