Characterizations of hemirings by (∈, ∈ ∨qk)-fuzzy ideals

In this paper we define (∈, ∈ ∨qk)-fuzzy h-sub hemirings, (∈, ∈ ∨qk)-fuzzy h-bi-ideals, (∈, ∈ ∨qk)-fuzzy h-quasi-ideals. We characterize h-hemiregular and h-intra-hemiregular hemirings by the properties of their (∈, ∈ ∨qk)-fuzzy h-ideals, (∈, ∈ ∨qk)-fuzzy h-biideals and (∈, ∈ ∨qk)-fuzzy h-quasi-ideals. Some of these characterizations are generalizations of the characterizations given in [36] [X. Ma, J. Zhan, Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings, Inform. Sci. 179 (2009) 1249–1268].