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

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