Fuzzy Posets With Fuzzy Order Applied to Fuzzy Ordered Groups

Branimir Šešelja, Andreja Tepavčević, Mirna Udovičić

In the framework of lattice valued structures we investigate fuzzy sub-posets of a given poset, in which the underlying set or$\backslash$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.