This　investigation　primarily　centers　on　the　reachable-set-based　bumpless　transfer　control　(BTC)　for　the　synchronization　of　switched　neutral-type　neural　networks　(SNNNs).　In　order　to　mitigate　the　conservatism　inherent　in　the　traditional　state-dependent　switching　strategies　(SDSSs)　and　combined　switching　strategies　(CSSs),　an　improved　CSS　leveraging　the　historical　information　of　neuron　states　and　neutral　delay　is　developed.　By　constructing　a　time-dependent　multiple　Lyapunov-Krasovskii　functional　(TDMLF)　technique,　a　less　conservative　criterion　for　reachable　set　estimation　(RSE)　is　first　established.　In　the　subsequent,　the　established　design　framework　is　further　employed　by　the　BTC　for　the　synchronization　of　SNNNs.　The　corresponding　synchronization　criterion　is　derived,　which　ensures　that　the　resultant　synchronization　error　influenced　by　bounded　external　inputs　can　be　confined　to　an　anticipated　bounded　set.　Also,　the　underlying　control　bumps　at　switching　instants　during　switching　instants　are　effectively　constrained　to　a　specific　level.　Ultimately,　the　practicability　and　superiority　of　the　proposed　design　framework　are　confirmed　via　two　simulation　examples.