TOPSIS

Use when

• A weighted sum hides that one option is mediocre everywhere and another is excellent on half.
• Criteria are measured in different units and you want a defensible normalisation.
• You need a ranking rather than a single winner.

Do not use when

• The audience will not follow the arithmetic. A weighted sum you can explain beats a better method nobody trusts.
• There are two options. The geometry adds nothing.

Inputs required

• A numeric matrix of options by criteria
• Weights
• Direction per criterion: more is better, or less is better

Procedure

1. 01

   Normalise the matrix

   Divide each cell by the root of the sum of squares in its column. This puts every criterion on a comparable scale without assuming a common unit.

2. 02

   Apply weights

   Multiply each normalised column by its weight.

3. 03

   Build the two anchors

   The ideal is the best value in each column; the anti-ideal is the worst. Neither is usually a real option — they are reference points.

4. 04

   Measure both distances

   For each option, compute the Euclidean distance to the ideal and to the anti-ideal.

5. 05

   Score by relative closeness

   Score is distance-to-worst divided by the sum of both distances, giving 0 to 1. Rank on that. An option scoring high is both near the best and far from the worst, which a weighted sum cannot distinguish.