| Abstract:Based on a t-norm, this paper introduces a notion of a fuzzy sub-semigroup degree, which is used to discuss the conditions that a fuzzy set of a semigroup is a fuzzy subsemigroup (resp. a fuzzy ideal etc.). First, it gives the definitions of a t-norm fuzzy subsemigroup degree, an intersection of two fuzzy subsets, a production of two fuzzy subsets and a t-norm fuzzy control, etc., re-spectively, investigates their properties and describes the conditions that a fuzzy subset of a semigroup is a fuzzy subsemigroup. Secondly, it discusses the t-norm fuzzy subsemigroup degree of a fuzzy left ideal (resp. a fuzzy right ideal, a fuzzy two-sided ideal and a fuzzy biideal), shows the conditions that a fuzzy set of a semigroup is a fuzzy left ideal (resp. a fuzzy right ideal, a fuzzy two-sided ideal and a fuzzy biideal). Finally, it checks the properties of a t-norm fuzzy subsemi-group degree under semigroup homomorphism. |
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