Fundamental homomorphism theorems of fuzzy subsemigroups

Abstract

The aim of this paper is to define and prove the properties of the homomorphism of fuzzy subsemigroup. This is the revised of the previous research has been done by the author. In this research we use different method to prove the fundamental theorem, i.e. using the properties of the alpha cut of the fuzzy subsemigroup. We got the result, based on the properties of alpha cut of a fuzzy subsemigroup, it is obtained a property that a semigroup is a fuzzy subsemigroup if and only if the alpha cut of the subsemigroup fuzzy is a semigroup. We also can prove that the fundamental homomorphism theorem of semigroup is valid for the fundamental homomorphism theorem of fuzzy subsemigroup.