We generalize the idea of (

,

)-fuzzy ordered semi-group and give the concept of (

,

)-fuzzy ordered

-semigroup. We show that (

,

)-fuzzy left (right, two-sided) ideals, (

,

)-fuzzy (generalized) bi-ideals, (

,

)-fuzzy interior ideals and (

,

)-fuzzy (1, 2)-ideals need not to be coincide in an ordered

-semigroup but on the other hand, we prove that all these (

,

)-fuzzy ideals coincide in a left regular class of an ordered

-semigroup. Further we investigate some useful conditions for an ordered

-semigroup to become a left regular ordered

-semigroup and characterize a left regular ordered

-semigroup in terms of (

,

)-fuzzy one-sided ideals. Finally we connect an ideal theory with an (

,

)-fuzzy ideal theory by using the notions of duo and (

)-fuzzy duo.