I'm a unsure whether you talk about a checkbox or a radio box. The title talks about a radio box, but the text (and the answers so far) talk about checkboxes. What these mean to me is below, but let's first turn to the undead state:
Unset State
I wonder why you need an "unset" state. Logically, there can never be an "unset bit". Either the bit is on, or it is off. The database cannot record "nothing", except when you designate a certain bit pattern (like 0x00) to mean "nothing". But what is the meaning of "nothing" in your business context? Does it mean "illegal" (then, validation should not have let it through to the database), or does it mean "undecided" (then, what is the meaning of it in the business process)?
On the UI, you might use a radio box group without a selection together with a validation routine to force the user to make a conscious choice. That's the "illegal" case above. That's appropriate if the choice is very important, and you don't want to rely on a default value which might have bad consequences.
If your program allows to save the nothing-selected state, you'll have to process the "undecided" value later in your business logic. You are adding another legal value, namely "undecided". If you need this, I would replace a two-item radio box group without a selection (o), such as
Preferred Delivery Option:
o air
o ground
with a three-item radio box group
Preferred Delivery Option:
* don't care
o air
o ground
and select (*) the first one initially.
I'd use the first alternative sparingly, and go for the second one if you have a real "undecided" state. I'd never use a checkbox with meaning UNSET - because the only third state usage I've seen so far is MAYBE:
Checkbox
A single control, usually a rectangular box with a label. The simple one has nothing in it (OFF), or a check mark in it (ON). There are tri-state ones as well, which often indicate the third state using an asterisk, but the meaning is usually MAYBE, and not UNSET. They're used when selecting items in a hierarchy: A higher-level item has state MAYBE when some of its children are ON and some others are OFF.
(The iPhone uses a different metaphor - it uses a slider; no third state possible.)
Radio Box (Group)
Must be a group of controls (grouped by background, frame, or whitespace), each usually visualized as a circle with a label. The circle is filled (ON) or empty (OFF), and in the entire group at most one control is ON, all others are OFF.