Fuzzy groups: Some group theoretic analogs. II (Q1091461)

The authors discuss successive notions of group theory and propose their fuzzy versions (order of fuzzy groups, fuzzy Abelian groups, fuzzy solvable groups, and prove theorems analogous to standard results of this theory (e.g. Cayley's theorem). Some differences are illustrated by examples (e.g. a fuzzy group of given order can have a proper subgroup of the same order). Other notions were discussed in previous papers by the same authors [cf. ibid. 34, 225-239 (1984; Zbl 0568.20002), and Part I, ibid. 39, 247-267 (1986; Zbl 0613.20001)].