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We introduce the notions of T L-ternary subsemigroup and T L-bi-ideals of a ternary semigroup. We redefine T L-ternary subsemigroup and T L-bi-ideals using T-product on L-sets .We introduce the notion of T-intersection of L-sets. We establish that T-intersection of two T L-bi-ideals is again a T L-bi-ideal. We establish necessary and sufficient conditions for a pre-image of L-set under homomorphism to be a T L-ideal.