The computational results of fuzzy subgroups of nilpotent finite ( pgroups ) involving multiple sums

Abstract

The theory of fuzzy sets has a wide range of applications, one of which is that of fuzzy groups. Part of its
applications is to provide formalized tools for dealing with the imprecision intrinsic to many problems.
Denote the number of chains of subgroups of a finite group G which ends in G by h(G). The method of
computing h(G) is based on the application of the Inclusion-Exclusion Principle. In this context , h(G)
is actually referred to as the number of district fuzzy subgroups for the finite nilpotent p-group. This
work is therefore designed as part to classify the nilpotent groups formed from the Cartesian products of
p-groups through their computations. In this paper, the Cartesian products of p-groups were taken to
obtain nilpotent groups. the explicit formulae is given for the number of distinct fuzzy subgroups of the
Cartesian product of the dihedral group of order eight with a cyclic group of order of an n power of two
for, which n is not less than three.