Decision Matrix

The decision matrix (commonly denoted as $M$) contains numerical values that describe how each alternative performs under various criteria.

• Rows represent alternatives (e.g., different options, projects, or solutions).
• Columns represent decision criteria (e.g., cost, quality, execution time).

	Criterion 1	Criterion 2	Criterion 3
Alternative A	100	4.5	200
Alternative B	80	3.8	250
Alternative C	120	4.2	180

Alternative

An alternative is one of the possible options or solutions considered in the decision-making process. Each alternative is evaluated across all decision criteria to determine its overall desirability or rank.

Examples of alternatives:

• Different products to buy,
• Investment options,
• Project plans.

Decision Criteria

A decision criteria is a measurable factor used to assess and compare alternatives. Each criterion reflects an important aspect of the decision problem and typically has an associated weight that indicates its relative importance. Examples of criteria:

• Cost,
• Efficiency,
• Environmental impact,
• User satisfaction.

The criterion type vector indicates the nature of each criterion, specifying whether the goal is to maximize (benefit) or minimize (cost) its value.

• It is typically represented using:

• 1 for benefit criteria (the higher, the better)

• -1 for cost criteria (the lower, the better)

Example:

$$T = [-1,\ 1,\ 1]$$

This means:

• Criterion 1 is a cost (to be minimized)
• Criterion 2 is a benefit (to be maximized)
• Criterion 3 is a benefit (to be maximized)