Using the Lukasiewicz 3-valued implication operator, the notion of an (

)-intuitionistic fuzzy left (right)

-ideal of a hemiring is introduced, where

. We define intuitionistic fuzzy left (right)

-ideal with thresholds (

) of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left (right)

-ideal with thresholds (

) and (

)-intuitionistic fuzzy left (right)

-ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a (

) (or (

) or (

)-intuitionistic fuzzy left (right)

-ideal of R if and only if A is an intuitionistic fuzzy left (right)

-ideal with thresholds (0, 1) (or (0, 0.5) or (0.5, 1)) of R respectively. It is also shown that A is a (

) (or (

) or (

))-intuitionistic fuzzy left (right)

-ideal if and only if for any

(0, 1] (or

(0, 0.5] or

(0.5, 1] ),

is a fuzzy left (right)

-ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left (right)

-ideal with thresholds (

) of R if and only if for any

, the cut set

is a fuzzy left (right)

-ideal of R.