The Remak-Krull-Schmidt Theorem on\\ Fuzzy Groups

In this paper we study a representation of a fuzzy subgroup \mu of a group G, as a product of indecomposable fuzzy subgroups called the components of \mu.  This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and some of their properties to prove this theorem. We illustrate with some examples.

Keywords:

Preferential equality , Fuzzy subgroup , Direct product , Indecomposable , Isomorphism , Lattice