Normalization

Vector Normalization: Euclidean column-norm scaling (L2 normalisation)

Hwang, C. L., Yoon, K. · 1981

Overview

Normalization (L2, unit-sphere projection). Output typically normalized_matrix (higher value = preferred).

Strengths

•Method-specific: Normalization (L2, unit-sphere projection)

Method assistant

Grounded explanations: it explains the method, it does not compute.

Edge cases

•See F.steps and D.parameters for NORM-VECTOR-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

•Bkz. NORM-VECTOR F.steps citation_anchor'lar ve P.verification_status.

Worked example

1.Adım 1 (F1): Step 1: For each criterion j compute the column Euclidean norm ||x_j||₂ = √(Σ_i x_ij²). Formül: \|\mathbf{x}_j\|_2 = \sqrt{\sum_{i=1}^{m} x_{ij}^2} Anchor: Hwang & Yoon 1981, p.130 Eq.(4.1) (pending PDF page verification)
2.Adım 2 (F2): Step 2: Divide each entry by its column norm: r_ij = x_ij / ||x_j||₂. Direction awareness (benefit/cost) is handled by the downstream ranking method, not during normalisation. Formül: r_{ij} = \frac{x_{ij}}{\sqrt{\sum_{k=1}^{m} x_{kj}^2}} Anchor: Hwang & Yoon 1981, p.130 Eq.(4.1) (pending PDF page verification)

How to cite

Hwang, C. L.; Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. Lecture Notes in Economics and Mathematical Systems, Vol. 186, Springer-Verlag. https://doi.org/10.1007/978-3-642-48318-9

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Worked example

1.Adım 1 (F1): Step 1: For each criterion j compute the column Euclidean norm ||x_j||₂ = √(Σ_i x_ij²). Formül: \|\mathbf{x}_j\|_2 = \sqrt{\sum_{i=1}^{m} x_{ij}^2} Anchor: Hwang & Yoon 1981, p.130 Eq.(4.1) (pending PDF page verification)

2.Adım 2 (F2): Step 2: Divide each entry by its column norm: r_ij = x_ij / ||x_j||₂. Direction awareness (benefit/cost) is handled by the downstream ranking method, not during normalisation. Formül: r_{ij} = \frac{x_{ij}}{\sqrt{\sum_{k=1}^{m} x_{kj}^2}} Anchor: Hwang & Yoon 1981, p.130 Eq.(4.1) (pending PDF page verification)