A decision matrix is a list of values in rows and columns that allows an analyst to systematically identify, analyze, and rate the performance of relationships between sets of values and information.
An MCDA problem, where there are M alternative options and each needs to be assessed on N criteria, can be described by the decision matrix which has N rows and M columns, or M × N elements, as shown in the following table.
Sums of scores may then be compared and ranked, to show the winning proposal.
For example, suppose Alternative i is "Car i", Criterion j is "Engine Quality" assessed by five grades {Excellent, Good, Average, Below Average, Poor}, and "Car i" is assessed to be “Excellent” on "Engine Quality" with a high degree of belief (e.g. 0.6) due to its low fuel consumption, low vibration and high responsiveness.
At the same time, the quality is also assessed to be only “Good” with a lower degree of belief (e.g. 0.4 or less) because its quietness and starting can still be improved.