Rotten wood: to fill or not to fill?
Below quoted advice is pinched from here, How to paint a wood house?


  If you encounter any damp, rotten, etc wood during the preparation stage, I highly recommend removing it. When doing so, cut 150mm (6inch) past the last sign of damage ie Get back to good, solid wood. Preferably re-patch with the same wood species.


In your particular situation (outdoors, horizontal surface) I would not recommend filling such a large hole with any kind of filler.

If you feel confident enough in your woodworking skills (or don't mind a challenge and want to learn something new), I say go with the above quoted method. If you were going to paint the wood, not stain it, I would be more likely to go with this method (paint can cover those little mistakes, where as stain is unforgiving).

That said it might just be easier (and cheaper) to remove the 4 pieces of wood completely and replace them with new timber, especially if you are going to stain the wood.