The fuzzy subgroup with thresholds was touched with implication-based fuzzy subgroup which builds up a connection between fuzzy logic and fuzzy algebra. But it is difficult to know whether a fuzzy set is a fuzzy (normal) subgroup with thresholds. In the present paper, an equivalent axiom of a fuzzy (normal) subgroup with thresholds is advanced by means of constructing a new fuzzy set so that we only need to determine whether the new fuzzy set is a fuzzy (normal) subgroup. Finally this paper considers its generalization under t-norm and t-conorm operations and discusses its properties.
Fuzzy subgroup, (∈∈ Vq) -fuzzy subgroup, T-Fuzzy subgroup with thresholds, T-Fuzzy normal subgroup with thresholds
