Euclidean Distance - L2 norm between two vectors in criterion space

Overview

d_E ≥ 0. d_E = 0 iff a = b. Sensitive to scale - normalise inputs before applying if criteria have different units or ranges. Most commonly used in TOPSIS as the separation measure.

Output

distance, lower is better

Data

Crisp, complete numeric matrix

Size

2+ alternatives, 3-12 criteria works best

Used for

Similarity assessment, clustering

How it works

1. 1

   Compute the Euclidean (L2) distance between vectors a and b: d_E = √Σ_j(a_j − b_j)².

   $$d_E(\mathbf{a},\mathbf{b})=\sqrt{\sum _{j=1}^n(a_j-b_j{)}^2}$$

   Hwang & Yoon 1981, p.130 Eq.(4.3) (separation measure; pending PDF page verification)

Edge cases and pitfalls

• Scale sensitivity: large-range criteria dominate; always normalise before computing distances in multi-criteria contexts.

Works with

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