Abstract
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.
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