For environmental modeling, remote sensing data play an important role in the data acquisition. Researchers must decide which type of sensor data best meet their preferences. Among the many alternative sensors available, the list of candidates has been reduced to three: LANTSAT $7($LS$7),$ GOES $($GS$),$ and TERRA $($TA$).$ The researchers have defined four objectives that impact their decision: $(1)$ cost of the data $($COST$),(2)$ time to deliver data $($TIME$),(3)$ resolution of the data collected $($RES$),$ and $(4)$ time for the sensor to return to the same spot cycle $($CT$).$ There was some disagreement as to how to define the importance of each objective in the preference set, so the researchers decided to define two sets of preferences, $P_1$ and $P_2.$The degree of membership of each alternative in the objectives is as follows:

$O_1=\{\frac{0\mathrm{.}2}{LS7},\frac{0\mathrm{.}9}{GS},\frac{0\mathrm{.}4}{TA}\},O_2=\{\frac{0\mathrm{.}6}{LS7},\frac{1}{GS},\frac{0\mathrm{.}2}{TA}\},O_3=\{\frac{1}{LS7},\frac{0\mathrm{.}6}{GS},\frac{0\mathrm{.}8}{TA}\},$

$O_4=\{\frac{0\mathrm{.}7}{LS7},\frac{0\mathrm{.}7}{GS},\frac{0\mathrm{.}2}{TA}\}.$

Find the decision for each preference.