The Fuji is semi-self fertile and will fruit if grown without a companion, but it fruits much better with a cross-pollinator nearby.

http://www.fruit-tree.com/applepollen.html

I believe the Fuji to be at least partially self-fruitful. I have a friend with one and I cannot see any apple or crab-apple tree anywhere else in his suburban neighborhood. Yet the tree bares fruit. Of course, I could be missing something.

In my experience outside of California all apples should be considered needing a pollinator. I have continually run into this question through the years. Although the lable may say self-fruitful if the tree originates(the grower)from the west coast and you live somewhere outside of this area than it is best to consider another variety to compliment your selection. This will also remove any dought(if you have no fruit) in 5 years that the variety that you planted is self-fruitful in your area.

"This will also remove any dought"

Thoughts of drought weighing heavy on your mind there, Ed? I know this desert where I farm stills gets a few summer rains, but not this year. I am betting we get little snow pack in the mountains this winter and so have a short irrigation water supply for next summer. It might seem early to think about this, but I sure see a dry trend. I need to overhaul the irrigation system on eight acres and I sure am thinking about drip instead of sprinkler.

It was late no doubt, what can I say.
I hope that many are as concerned as you are about the lack of water. A dry trend and the greater demand for water could pose problems in the coming years. Any and all considerations to conserve water need to become common practice for commercial and home gardener alike.