$3\mathrm{.}11.$ A new optical microscope camera uses a lookup table to relate voltage readings

$($which are related to illuminance$)$ to exposure time. To aid in the creation of this

lookup table, we need to determine how much time the camera should expose the

pictures at a certain light level. Define a fuzzy set "around $3$ volts" on a universe

of voltage readings in volts

$V{}_{15}=\{\frac{0\mathrm{.}1}{2\mathrm{.}98}+\frac{0\mathrm{.}3}{2\mathrm{.}99}+\frac{0\mathrm{.}7}{3}+\frac{0\mathrm{.}4}{3\mathrm{.}01}+\frac{0\mathrm{.}2}{3\mathrm{.}02}\},($ volts $)$

and a fuzzy set "almost $\frac{1}{10}$ second" on a universe of exposure time in seconds

$T_{16}=\{\frac{0\mathrm{.}1}{0\mathrm{.}05}+\frac{0\mathrm{.}3}{0\mathrm{.}06}+\frac{0\mathrm{.}3}{0\mathrm{.}07}+\frac{0\mathrm{.}4}{0\mathrm{.}08}+\frac{0\mathrm{.}5}{0\mathrm{.}09}+\frac{1\mathrm{.}0}{0\mathrm{.}1}\},(seconds)$

$($a$)$ Find $R=VT.$

Now define a third universe of "stops." In photography, stops are related to

making the picture some degree lighter or darker than the "average" exposed

picture. Therefore, let Universe of Stops $=\{0,0\mathrm{.}5,1\}($stops$).$ We will define a

fuzzy set on this universe as

$Z=$ a little bit lighter $=\{\frac{0\mathrm{.}1}{0}+\frac{0\mathrm{.}7}{0\mathrm{.}5}+\frac{0\mathrm{.}3}{1}\}$

$($b$)$ Find $S=TZ.$

$($c$)$ Find $M=R$@$S$ by max$-$min composition.

$($d$)$ Find $M=R$@widetilde$(S)$ by max$-$product composition.