There are a couple of reasons why this is happening, both of which are related to the 'Units' of the components.
First, when you create the uibuttongroup:
bg(i).bg = uibuttongroup(fig,'Title',['Song' int2str(i)], 'Visible','off',...
'Position',[0 y 1 0.7/TotalSong],...
'Units', 'normalized');
you have to specify the 'Units' before the 'Position':
bg(i).bg = uibuttongroup(fig,'Title',['Song' int2str(i)], 'Visible','off',...
'Units', 'normalized', ...
'Position',[0 y 1 0.7/TotalSong]);
If you put 'Position' first, MATLAB interprets that position in terms of the default units, which is pixels, and then converts that pixel position into normalized Units when it parses the 'Units','normalized' input arguments. Specifying 'Units' first prevents this conversion.
Making that change should make the uibuttongroups show up, but you will still see no actual uiradiobuttons because there's also a problem with their Units/Positions.
uiradiobuttons' Positions are in pixel units, and there's nothing you can do - as far as I know - to change their units (they don't have a 'Units' property at all). But here, you appear to want to set their Positions as if their Units are 'normalized', so to do that, you have to figure out what the position (in pixels) of a uiradiobutton should be, given the position of the parent uibuttongroup (and, since that is in 'normalized' units, you also need the position of the uifigure).
Here's how the corresponding code to do that would look:
TotalSong = 3;
TotalOptionNo = 5;
fig = uifigure();
fig_wh = fig.Position([3 4]); % uifigure width and height in pixels
bg_wh = [1 0.7/TotalSong]; % uibuttongroup width and height in 'normalized' units
rb_wh = fig_wh.*bg_wh.*[0.1 0.5]; % uiradiobutton width and height in pixels
for i = 1:TotalSong
y = 1-(1-0.7/TotalSong)*i/TotalSong;
if y<0
y = 0;
end
% specify Units before Position:
bg(i).bg = uibuttongroup(fig,'Title',['Song' int2str(i)], 'Visible','off',...
'Units', 'normalized', ...
'Position',[0 y bg_wh]);
for k = 1:TotalOptionNo
% uiradiobutton x-coordinate (left), in pixels:
rb_x = (1-0.3)*k/TotalOptionNo*bg_wh(1)*fig_wh(1);
rb(k).(['bg' int2str(i)]) = uiradiobutton(bg(i).bg,...
'Value', 0,...
'Text', int2str(k),...
'Position',[rb_x 0 rb_wh]);
end
bg(i).bg.Visible = 'on';
end
