This book presents an up-to-date account of research in important topics
of fuzzy group theory. It concentrates on the theoretical aspects of
fuzzy subgroups of a group. It includes applications to abstract
recognition problems and to coding theory. The book begins with basic
properties of fuzzy subgroups. Fuzzy subgroups of Hamiltonian, solvable,
P-Hall, and nilpotent groups are discussed. Construction of free fuzzy
subgroups is determined. Numerical invariants of fuzzy subgroups of
Abelian groups are developed. The problem in group theory of obtaining
conditions under which a group can be expressed as a direct product of
its normal subgroups is considered. Methods for deriving fuzzy theorems
from crisp ones are presented and the embedding of lattices of fuzzy
subgroups into lattices of crisp groups is discussed as well as deriving
membership functions from similarity relations. The material presented
makes this book a good reference for graduate students and researchers
working in fuzzy group theory.