Use Arduino Uno as multiplexer latched output

I seems you want to control some valves ? (type, voltage, current) ?
With a microcontroller with limited outputs ? (is it already used for other things) ?
You have already decided you need relays for that ?

Why do you think a multiplexer is the answer.
Time division muxing is ok for LEDs (persistence of vision), but not for relays.
A shift register could be a better solution (depending on the rest of the hardware).
Post links to the valves.
Leo..