Abstract
In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is char- acterized. Furthermore, the Fundamental Homomorphism Theorem is estab- lished. Finally, it is proved that the class of all fuzzy convex lattice-ordered subgroups of a lattice-ordered group G forms a complete Heyting sublattice of the lattice of fuzzy subgroups of G.
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