Linear Max Normalization: division by column maximum (benefit) or column minimum over value (cost)

Overview

Normalization (linear-max, ratio-based). Output typically normalized_matrix (higher value = preferred).

Strengths

• •Method-specific: Normalization (linear-max, ratio-based)

Edge cases

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

Common pitfalls

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

Worked example

1. 1.Adım 1 (F1): Apply: benefit criterion j → r_ij = x_ij / x_j^max. Cost criterion j → r_ij = x_j^min / x_ij. Result: best alternative scores 1 in both cases. Formül: r_{ij} = \begin{cases} x_{ij}/x_j^{\max} & j \in J^{+} \\ x_j^{\min}/x_{ij} & j \in J^{-} \end{cases} Anchor: Fishburn 1967, p.538 (ratio normalisation; pending PDF page verification)

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