For the life of my car that I've had it I've had a problem with the fuel gauge not reading correctly. But lately I've been getting a low fuel warning, going to fill up and only filling it a little more than half way
My car has 112000 miles.
My car has an automatic transmission.
This is a simple mechanical failure. Located on the fuel pump is a float (quite like the one in your toilet) that sends a digital reading to the instrument cluster on your dashboard. This float can become clogged with debris and is prone to other mechanical failures that prevent it from moving freely.
Some vehicles can experience a failed electrical connection, but that typically makes the entire gauge inoperable. You will likely need to drop the tank and replace the fuel pump altogether. The fuel pump itself may or may not be bad itself, but the pump and float are all part of the same module.
I recommend having a certified technician, such as one from YourMechanic, determine the exact source of the fuel misreading and replace the fuel pump if needed.