Ranking method · Hwang & Yoon, 1981

TOPSIS

Technique for Order of Preference by Similarity to Ideal Solution

The best alternative is the one closest to the ideal solution and farthest from the worst one.

How it works

1. Normalize the decision matrix so criteria with different units become comparable (vector normalization).
2. Multiply each column by its criterion weight.
3. Construct the ideal solution (best value on every criterion) and the anti-ideal solution (worst value on every criterion).
4. Measure each alternative's Euclidean distance to both.
5. Score each alternative by relative closeness C* = D⁻ / (D⁺ + D⁻); rank by descending C*.

Use it when

• You have quantitative data and want a single, easy-to-read score per alternative.
• You need a complete best-to-worst ranking rather than a shortlist.
• Stakeholders want a method that is simple to explain and audit.

Watch out for

• Adding or removing an alternative can reorder the others (rank reversal).
• Results depend on the normalization scheme; extreme outliers distort distances.

Parameters

No extra parameters only weights and optimization directions.

Cite the method

Hwang, C.-L., & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag.

@book{hwang1981multiple,
  author    = {Hwang, Ching-Lai and Yoon, Kwangsun},
  title     = {Multiple Attribute Decision Making: Methods and Applications},
  publisher = {Springer-Verlag},
  address   = {Berlin, Heidelberg},
  year      = {1981},
  doi       = {10.1007/978-3-642-48318-9}
}