On fuzzy convex lattice-ordered subgroups

Document Type : Research Paper


Department of Mathematics, Bojnord University, Bojnord, Iran


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 characterized. Furthermore, the Fundamental Homomorphism Theorem is established. 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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