The most important thing it lets you do is combine and compare factors in nonlinear but intuitive ways.
The aircon example isn't really that great, to be honest, because there's only one rule and only one action you can take. If you add in "how full is the room" (and letting that be tuned for room size), an automated window vent, the outside temperature, and some sort of air quality reading, you can see how the job of making a room tolerable to be in starts to combine factors in interesting ways. https://en.wikipedia.org/wiki/Fuzzy_associative_matrix and https://en.wikipedia.org/wiki/Defuzzification are things I'm sure your course would have covered, but that's where I'd point at as a start.
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The most important thing it lets you do is combine and compare factors in nonlinear but intuitive ways.
The aircon example isn't really that great, to be honest, because there's only one rule and only one action you can take. If you add in "how full is the room" (and letting that be tuned for room size), an automated window vent, the outside temperature, and some sort of air quality reading, you can see how the job of making a room tolerable to be in starts to combine factors in interesting ways. https://en.wikipedia.org/wiki/Fuzzy_associative_matrix and https://en.wikipedia.org/wiki/Defuzzification are things I'm sure your course would have covered, but that's where I'd point at as a start.