Abstract
The notion of a fuzzy subgroup of G was introduced. It was shown that although such classes look different, each fuzzy subgroup in either was isomorphic to one in the other. In addition, it was shown that a fuzzy subgroup satisfies the definition of fuzzy subgroup with T='minimum' if and only if it was a fuzzy subgroup generated of a very special type. This paper shows how the abstract pattern recognition problems developed can be used to examine the faithfulness of a device F which decodes message transmitted across a noisy channel.