A per pixel edge fade?

I seriously hope someone knows a good way to go about this...

i have an image in the shape of a circle, the background is transparent.

I want to fade the edges of the circle into transparency, BUT the only results i get are actual transparency values per pixel. aka a soft fade (such as a blur or from a eraser brush)

But what I really need is a per pixel fade: either a pixel is there or it is removed. so the edges would miss a lot of pixels and towards the center the amount of pixels deleted would have to be less and less till its solid in the central area.

Any help would be greatly appreciated!