Photoshop Question

I have a gif logo which was on a pink background, I wanted to change the background color, but the logo has a thin pink border around it. The pink border fades from white (the color of the logo) to dark pink (the color of the background), which basiacally makes it blend in with the background instead of looking jagged. What I want to do is make the pink pixels around the logo transparent, but I want each pixels transparency to coorelate to the shade of pink it is. Then I plan to save it as a png, and then I can put the logo on any color background and it will blend it. Anyone know how I can do this?