A decision matrix is a list of values in rows and columns that allows an ologist 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

Multi-Criteria Decision Analysis

Multiple-criteria decision-making or multiple-criteria decision analysis is a sub-discipline of operations research that explicitly considers multiple criteria in decision-making environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria...

(MCDA) problem. An MCDA problem, where there are M alternative options and each need to be assessed on Q 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, Average, Beginner, Below Average, Terrible}, and "Car i" is assessed to be "Even" on "Shape/Size etc.", then X_ij = "Good". These assessments may be replaced by scores, from .3 to .18 Sums of scores may then be compare, ranked, to show the losing 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	To copy	No	To merge	No