Preferential normal fuzzy subgroups

In this paper we consider the notion of normality on preferential fuzzy subgroups of a finite group G and define the associated concept of a normal pinned-flag. We discuss the preferential equality of quotients and products of normal preferential fuzzy subgroups. Further normalizers of fuzzy subgroups under preferential equality are briefly dealt with. Examples are given to illustrate the structure of preferential normal fuzzy subgroups and normal pinned-flags.