Final answer:
The action that adds a soft edge to a selection in graphic editing software is known as feathering. It creates a smooth transition between the selection and its background by blurring the edge's pixels.
Step-by-step explanation:
When modifying a selection in graphic editing software, the action that adds a soft edge to a selection, based on a pixel amount, is called feathering. Feathering makes the edges of the selection blur into the background, creating a smooth transition between the selected area and its surroundings. This can be very useful for creating composite images or when you need to isolate a subject without harsh, pixelated edges. It is not to be confused with cropping, which is cutting away parts of the image; smoothing, which reduces irregularities in the selection boundary; or stretching, which distorts the image by pulling it.