Abstract
In this paper, the relations between $ L $-fuzzy semi-prime (respectively, $ L $-fuzzy prime) ideals of a poset and $ L $-fuzzy semi-prime (respectively, $ L $-fuzzy prime) ideals of the lattice of all ideals of a poset are established. A result analogous to Separation Theorem is obtained using $ L $-fuzzy semi-prime ideals.
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