This problem presents a fuzzy logic system to control the speed of a fan based on the room temperature error and its rate of change.

$$ Inputs, Outputs, and Variables:

$$ Input Variables:$$ Error $($E$)$: $[-5,5]$C$,$ Change in Error $($CE$)$: $[-3,3]$C$/$min

$$ Output Variable:$$ Fan Speed $($FS$)$: $[0,10]$

$$ Rule Base :

$$ If Error is Negative large and Change in Error is Decreasing fast, then Fan Speed is Fast.

$$ If Error is Zero and Change in Error is Constant, then Fan Speed is Medium.

$$ If Error is Positive Large and Change in Error is Increasing Fast, then Fan Speed is Slow.

$1.$ Formulate fuzzy rules in IF$-$THEN format.

$2.$ Calculates the crisp output by computing the centroid of the areas under the fuzzy membership functions if Given E $=2$ and CE $=-1\mathrm{.}5.$