I'm taking your question to be "How plausible is a world with intelligent fungi?"
On the face of it, it seems extremely unlikely. Plants, animals and fungi seem to have diverged from a common ancestor at about the same time.
They diverged because they adopted different life-styles: plants photosynthesized (and thus didn't need mobility or many senses), animals ate plants and fungi and each other (and thus needed mobility and keen senses) and fungi adapted to a middle ground of living on existing chemical gradients (e.g., by eating decaying plant and animal matter), which also did not necessitate movement or keen senses.
Could a fungus develop animal-like characteristics? Sure, evolution is ingenious. But it is very, very unlikely because evolution doesn't make things like senses and muscles don't just pop into being; rather they develop incrementally out of something else. And in a world already inhabited by animals, it's hard to see how the animal niche would have enough room for fungi to evolve into it also.
Had animals never evolved, might fungi have filled that active predator niche? Sure. But the result would necessarily not look at all like a fungus. A fungus is a very low-energy organism, and to evolve movement and senses, it would need to develop all the same adaptations (air supply, muscles, differentiated organs) that allow animals to move and sense. The very tissues would have to change right down to the cellular level. So they would start to resemble animals in most ways, and mushrooms not much at all.
Finally, intelligence. In a world of animals where the fungi never evolve movement or keen senses, it is very, very unlikely that intelligence would arise, since it is energetically very expensive and would not contribute much to survival of a sessile creature. ("How much intelligence do you need to sneak up on a rotted log?")
Additionally, it seems likely that intelligence evolves most readily in social creatures, and, once more, if your fungoid were social it would again require a biology much more like that of an animal than a mushroom.
So: Intelligent creatures evolved from fungi? Perfectly plausible, but they would look and act like animals and it would probably take a deep knowledge of biology and a lot of work to demonstrate that there was a toadstool far back in their evolutionary tree.