The Group of L-Fuzzy Homeomorphisms and the Group of Permutations of the Ground Set

In this paper we study some relations between the group of L-fuzzy homeomorphisms of an L-fuzzy topological space X and the group of permutations of the ground set X. In contrast with the results in general topology, it is proved that the subgroups generated by cycles and proper normal subgroups can be represented as groups of L-fuzzy homeomorphisms for some L-fuzzy topology on X. The relation between the group of L-fuzzy homeomorphisms and the group of homeomorphisms of the associated topology is also discussed.