Normalization

Logarithmic Normalization: log-ratio column normalisation for multiplicative aggregation contexts

Zavadskas, E. K., Turskis, Z. · 2008

Overview

Normalization (logarithmic, multiplicative). Output typically normalized_matrix (higher value = preferred).

Strengths

•Method-specific: Normalization (logarithmic, multiplicative)

Method assistant

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

Edge cases

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

Common pitfalls

•Bkz. LOGARITHMIC-NORMALIZATION F.steps citation_anchor'lar ve P.verification_status.

Worked example

1.Adım 1 (F1): Benefit criterion j: r_ij = ln(x_ij) / ln(Π_k x_kj) = ln(x_ij) / Σ_k ln(x_kj). Cost criterion j: first compute benefit-normalised values, then apply r_ij = (1 − r_ij^benefit) / Σ_k (1 − r_kj^benefit). Formül: r_{ij} = \frac{\ln x_{ij}}{\ln \prod_{k=1}^{m} x_{kj}} = \frac{\ln x_{ij}}{\sum_{k=1}^{m} \ln x_{kj}},\quad j\in J^{+};\quad r_{ij} = \frac{1 - r_{ij}^{+}}{\sum_k (1-r_{kj}^{+})},\quad j\in J^{-} Anchor: Zavadskas & Turskis 2008, p.306 Eqs.(1)-(2) (pending PDF page verification)

How to cite

Zavadskas, E. K.; Turskis, Z. (2008). A new logarithmic normalization method in games theory. Informatica. https://doi.org/10.15388/informatica.2008.215

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Worked example

1.Adım 1 (F1): Benefit criterion j: r_ij = ln(x_ij) / ln(Π_k x_kj) = ln(x_ij) / Σ_k ln(x_kj). Cost criterion j: first compute benefit-normalised values, then apply r_ij = (1 − r_ij^benefit) / Σ_k (1 − r_kj^benefit). Formül: r_{ij} = \frac{\ln x_{ij}}{\ln \prod_{k=1}^{m} x_{kj}} = \frac{\ln x_{ij}}{\sum_{k=1}^{m} \ln x_{kj}},\quad j\in J^{+};\quad r_{ij} = \frac{1 - r_{ij}^{+}}{\sum_k (1-r_{kj}^{+})},\quad j\in J^{-} Anchor: Zavadskas & Turskis 2008, p.306 Eqs.(1)-(2) (pending PDF page verification)