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In this paper our attempt is to extend the notion of essential fuzzy ideals of rings to T-fuzzy essential ideals. Various properties on T-fuzzy essential ideals are established. Some results are being discussed which establish necessary and sufficient condition between T-fuzzy essential ideal in fuzzy set theory and essential ideal in crisp set theory. Moreover it is proved that if µ, andare non-zero T-fuzzy left ideals of R such that µ ⊆  ⊆ , then µ ⊆e(T)  if and only if µ ⊆e(T)  ⊆e(T) .

ON T-FUZZY ESSENTIAL IDEALS OF RINGS