Fuzzy Ideals Extensions in Semigroups

Abstract

In this paper, we shall introduce the notions of fuzzy ideal extension property, strongly fuzzy extension property and fuzzy property of a semigroup S. We also discuss the relations of these fuzzy ideal extension poperties and some properties of semigroups with the fuzzy ideal extension prorerty. Furthermore, we prove that a semigroup has the ideal extension property if and only if S has the strongly fuzzy ideal extension property. As an application of the results of this paper, we obtain characterizations of cyclic semigroups