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Hello:

  I've been trying to figure out how to blend the edges of a G'mic generated annular steiner chain with round tiles. I've tried feathering by creating a channel selection then inverting it- didn't work.  I then tried a gradient and that didn't work; blurs (gaussian, etc.) affect the whole image and I simply want to blur the edges of the round tiles (circles).

I'm using gimp 2.10 on win 8 64bit. 

Any guidance would be greatly appreciated.

A few possibilities, is it like this

[attachment=5991]

Layer > transparency > alpha to selection
Select > shrink selection
Select >  invert
Selection > Feather (if you want a soft inner edge)
Layer Alpha lock on (if you want an outer hard edge)
Filters gaussian blur
Turn selection off

Workflow as rich mentioned and then : Filters / Blur / Focus Blur
[attachment=5992]