Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings

A new kind of generalized fuzzy h-ideals of a hemiring, namely, the image-fuzzy h-bi-ideal (resp., h-quasi-ideal) is studied and the relationships between these generalized fuzzy h-ideals are described. Some characterization theorems of prime and semiprime image-fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring are also given. In particular, we show that the h-hemiregular hemirings and h-intra-hemiregular hemirings can be described by using some of their generalized fuzzy h-ideals. Finally, the implication-based fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring are considered.