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We first give some useful characterizations of regular semigroups and right weakly regular semigroups by the properties of their bi-ideals, interior ideals, left ideals and right ideals. Based on these characterizations, we also characterize regular semigroups and right weakly regular semigroups by the properties of their (∈,∈∨ qk)-fuzzy (generalized) bi-ideals,(∈,∈∨ qk)-fuzzy interior ideals,(∈,∈∨ qk)-fuzzy left ideals and (∈,∈∨ qk)-fuzzy right ideals.