Decision Matrix

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. Elements of a decision matrix show decisions based on certain decision criteria. The matrix is useful for looking at large masses of decision factors and assessing each factor’s relative significance. Decision matrix is used to describe a multi-criteria decision analysis (MCDA) problem. An MCDA problem, where there are M alternative options and each need to be assessed on N criteria, can be described by the decision matrix which has M rows and N columns, or M × N elements, as shown in the following table. Each element, such as X_ij, is either a single numerical value or a single grade, representing the performance of alternative i on criterion j. For example, if alternative i is "car i", criterion j is "engine quality" assessed by five grades {Exceptional, Good, Average, Below Average, Poor}, and "Car i" is assessed to be "Good" on "engine quality", then X_ij = "Good". These assessments may be replaced by scores, from 1 to 5. Sums of scores may then be compared and ranked, to show the winning proposal.

Example of Comparison

	Criterion 1	Criterion 2	...	Criterion N
Alternative 1	x11	x12	...	x1N
Alternative 2	x21	x22	...	x2N
...	...	...	Xij = Good	...
Alternative M	xM1	xM2	...	xMN
Sum
Rank
Status		No		No

A belief decision matrix is similar, except that any given matrix entry may have several different values, together with a "confidence" measure for that value. So, for example, a car engine may be ranked as "excellent" for fuel economy (here, with a "confidence" or importance of 0.6) but merely "good" for fuel economy (with a confidence/importance of 0.4). In this sense, a belief decision matrix generalizes an ordinary decision matrix by allowing multiple values for a given entry.