Wooden plank floor on thick joists noise reduction

Hello guys. Could you please advise me?

This it the gallery of my house. The wooden joists are 6x4 inches (10x16 cm). I leveled them good.
I would like to install almost 2 inch thick pine/fir wooden planks on it. I would like to minimize vibrations and squeaking on the floor so I thought I could lay 2 mm rubber on the joists (⁵/₆₄ of an inch) and lay the planks on that but not to screw them on to the joists. I would take additional 2x4 (coloured red) and connect the planks with those and everything would float on the joists. Is this a good idea or should I just screw the planks on the joists? or should I use cork rather than rubber?

I hope I am being clear, not a native English speaker.

Every advice is very useful. thank you
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I think you might create a new problem in solving the old one. Rubber compresses, so you might find that the edges of the planks depress and rub against each other and squeak when people walk on them. Depending on what rubber you use, it will probably degrade over time and maybe worsen the squeak. Cork is a natural material, but the same probably applies to it to a greater or lesser extent. You might be better off screwing the planks onto the joists, but if the space under the joists in your picture stays open you might be better off in the long term screwing timber or angle iron to your joists and pulling the planks down onto the timber or angle iron from below through the timber or angle iron. It's the same way that some problem noisy floorboards are dealt with in established houses. This also gives you a clear surface on the planks in your room and the ability to tighten the screws from below if there is movement.