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 homeomor phisms of an L-fuzzy topological space X and the group of permutations of t he ground set X. In contrast with the results in general topology, it is pr oved that the subgroups generated by cycles and proper normal subgroups can be represented as groups of L-fuzzy homeomorphisms for some L-fuzzy topolo gy on X. The relation between the group of I-fuzzy homeomorphisms and the g roup of homeomorphisms of the associated topology is also discussed. (C) 20 00 Academic Press.