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In the framework of lattice valued structures we investigate fuzzy sub-posets of a given poset, in which the underlying set or$\setminus$and the order are fuzzy and the reflexivity is specially defined. We introduce and investigate particular fuzzy sub-posets, e.g, fuzzy up--sets and down--sets, fuzzy convex sub--posets, fuzzy intervals etc. We describe the structure of the lattice of all fuzzy orders contained in a given crisp ordering. Then we apply these in defining a fuzzy ordered subgroup of an ordered group. Main features of fuzzy ordered subgroups are introduced and investigated like fuzzy positive and negative cone and fuzzy convex subgroups.

Fuzzy posets with fuzzy order applied to fuzzy ordered groups