In different literatures, we have found several generalizations of ideals and filters of a lattice to an arbitrarily partially ordered set which has been studied by different scholars . In this thesis we introduce several generalizations of L-fuzzy ideals and filters of a lattice to an arbitrarily partially ordered set whose truth values are in a complete lattice satisfying the infinite meet distributive law. These are: L-fuzzy closed ideal and filter of a poset, L-fuzzy Frink ideal and filter of a poset, L-fuzzy ideal and filter of a poset in the sense of Halaš, L-fuzzy semi ideals and filters of a poset, L-fuzzy V-ideals and V-filters of a poset and m-L-fuzzy ideals and filters of a poset, where m is any cardinal number. All the definitions of L-fuzzy ideals and filters of a poset that we introduce in this thesis are generalizations of the notions of L-fuzzy ideals and filters of a lattice. We also study and establish some characterizations of them and we prove that the set of all L-fuzzy ideals of a poset forms a complete lattice with respect to point-wise ordering. Next, by choosing the L-fuzzy ideals and filters of a poset in the sense of Halaš as an L-fuzzy ideals of a poset, we introduce the notion of L-fuzzy prime ideals, prime Lfuzzy ideals, maximal L-fuzzy ideals and L-fuzzy maximal ideals. We also study and give sufficient conditions for the existence of L-fuzzy prime ideals and prime L-fuzzy ideals in the lattice of all L-fuzzy ideals of a poset. Lastly, we introduce the concept of L-fuzzy semi-prime ideals in a general poset. Characterizations of L-fuzzy semi-prime ideals in posets as well as characterizations of an L-fuzzy semi-prime ideal to be L-fuzzy prime ideal are obtained. Also, the relations between the L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of a poset and the L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of the lattice of all ideals of a poset are established. We also extend and prove an analogue of Stone’s Theorem for finite posets, which has been studied by V. S. Kharat and K. A. Mokbel[35] using L-fuzzy semi-prime ideals.