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I have to "fix" some 50 micron tungsten wire to copper/brass.
Note that this is on a scale that is too small for a mechanical connection to be used (screws, clamps, etc.)
Assuming you need a Tungsten wire for high temperature heating, then :
Use a tiny copper pipe, hose and crimp to the filament ends. Screw or solder the copper terminals to PCB or whatever you need. In such way you will have a good contact which won't excessively heat when the filament will be turned on. In place of copper pipe you can use also a wrapped copper foil, but firmly crimping the copper will give best performance.
I would first look at welding under a microscope using a tweezer handpiece.
If you don't have access to such a welder with fine low current control, contact the makers and they should be able to help you. The machine should be under $10K for a good one.
You could also consider using a platinum plated tungsten wire, which would be more resistant to corrosion and easier to deal with. They are used in some kinds of instrumentation.
A small spot welder of the type used for thermocouple wires? I believe Omega sells systems like this.
Tungsten can also be soldered (at gas-torch temperatures) using silver-based "hard" solders and fluoride-based silver-solder flux.
