Note: [1] This work is supported by National Natural Science Foundation of China (11901358), and Shandong Province Social Science Planning Research Project(14DGLJ06).
Abstract: By means of a fuzzy binary operation defined on partially ordered sets, a new kind of ordered fuzzy group is proposed in this paper. Some properties of this ordered fuzzy group are studied. Following that, its substructures, such as subgroup and convex subgroup, as well as its homomorphisms, along with their properties are explored. It is shown that each family of these substructures forms a convex structure, where the convex hull of a subset is exactly the (convex) subgroup generated by itself, and the homomorphisms between two ordered fuzzy groups are convexity-preserving mappings between the corresponding convex spaces. In addition, when these substructures are extended to fuzzy setting, several L-convex structures are constructed and investigated.
