The present paper contains the sufficient condition of a fuzzy semigroup to be a fuzzy group using fuzzy points. The existence of a fuzzy kernel in
semigroup is explored. It has been shown that every fuzzy ideal of a semigroup
contains every minimal fuzzy left and every minimal fuzzy right ideal of semigroup.
The fuzzy kernel is the class sum of minimal fuzzy left (right) ideals of a semigroup.
Every fuzzy left ideal of a fuzzy kernel is also a fuzzy left ideal of a semigroup. It
has been shown that the product of minimal fuzzy left ideal and minimal fuzzy
right ideal of a semigroup forms a group. The representation of minimal fuzzy left
(right) ideals and also the representation of intersection of minimal fuzzy left ideal
and minimal fuzzy right ideal are shown. The fuzzy kernel of a semigroup is basically
the class sum of all the minimal fuzzy left (right) ideals of a semigroup. Finally
the sufficient condition of fuzzy kernel to be completely simple semigroup has been
proved
