On Minimal Fuzzy Ideals of Semigroups

Abstract EN

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.