On Cubic Fuzzy Groups and Cubic Fuzzy Normal Subgroups

Abstract

In this paper, the notions of cubic fuzzy groups and cubic fuzzy normal subgroups are introduced. The internal, external of cubic sets, (P-,R-) order, (P-,R-) intersection and (P-,R-) union of cubic fuzzy groups are investigated and some related properties were obtained. It is proved that a cubic fuzzy group which is both (internal, external) cubic set. Also we provide condition on cubic fuzzy group to be an internal cubic set. We show that (P-,R-) intersection and (P-,R-) union of cubic fuzzy groups are also cubic fuzzy groups. Also the (P-,R-) intersection, (P-,R-) union of cubic fuzzy normal subgroups are proved to be cubic fuzzy normal subgroup.