Assume that a decision maker has to make a choice between three types of cars. Chevy, Honda, and Ford. Based on three criteria: comfort, MPG, and style.
The row averages for criteria is summarized in the following column vector: $$\left[ \begin{array} { l }
.3 \
.5 \
.2
\end{array} \right]$$
The first row of the following matrix represents Chevy, the second row represents Honda, and the third row represents Ford.
The preference matrix for the three types of cars is given as follows: $$\left[ \begin{array} { l l l }
.5 & .2 & .2 \
.3 & .7 & .2 \
.2 & .1 & .6
\end{array} \right]$$
Compute the overall score for each decision alternative (car). Which choice does the decision maker prefer?
A) Chevy
B) Honda
C) Ford
D) Honda and Chevy are equally preferred.

Question

Assume that a decision maker has to make a choice between three types of cars. Chevy, Honda, and Ford. Based on three criteria: comfort, MPG, and style.
The row averages for criteria is summarized in the following column vector: $$\left[ \begin{array} { l } 
.3 \
.5 \
.2
\end{array} \right]$$
The first row of the following matrix represents Chevy, the second row represents Honda, and the third row represents Ford.
The preference matrix for the three types of cars is given as follows: $$\left[ \begin{array} { l l l } 
.5 & .2 & .2 \
.3 & .7 & .2 \
.2 & .1 & .6
\end{array} \right]$$
Compute the overall score for each decision alternative (car). Which choice does the decision maker prefer?
A) Chevy
B) Honda
C) Ford
D) Honda and Chevy are equally preferred.

Quizplus · Accepted Answer

To find the overall score for each car, multiply the criteria weights by the preference scores for each car and sum them up. For Chevy: $0.3 \times 0.5 + 0.5 \times 0.2 + 0.2 \times 0.2 = 0.15 + 0.1 + 0.04 = 0.29$. For Honda: $0.3 \times 0.3 + 0.5 \times 0.7 + 0.2 \times 0.2 = 0.09 + 0.35 + 0.04 = 0.48$. For Ford: $0.3 \times 0.2 + 0.5 \times 0.1 + 0.2 \times 0.6 = 0.06 + 0.05 + 0.12 = 0.23$. Honda has the highest score (0.48), so it is the preferred choice.

Assume That a Decision Maker Has to Make a Choice [.3.5.2]\left[ \begin{array} { l } .3 \\.5 \\.2\end{array} \right]​.3.5.2​​

Assume That a Decision Maker Has to Make a Choice $\left[ \begin{array} { l } .3 \\.5 \\.2\end{array} \right]$