Semigroups characterized by (∈,∈∨qk)(∈,∈∨qk)-fuzzy ideals

Generalizing the notions of (∈,∈∨q)(∈,∈∨q)-fuzzy ideal, (∈,∈∨q)(∈,∈∨q)-fuzzy quasi-ideal and (∈,∈∨q)(∈,∈∨q)-fuzzy bi-ideal, the concepts of (∈,∈∨qk)(∈,∈∨qk)-fuzzy ideal, (∈,∈∨qk)(∈,∈∨qk)-fuzzy quasi-ideal and (∈,∈∨qk)(∈,∈∨qk)-fuzzy bi-ideal are defined. Different classes of semigroups are characterized by the properties of these fuzzy ideals.