Normalization

Min-Max Normalization: linear rescaling of each criterion column to [0, 1]

Hwang, C. L., Yoon, K. · 1981

Overview

Normalization (linear, range-scaling). Output typically normalized_matrix (higher value = preferred).

Strengths

•Method-specific: Normalization (linear, range-scaling)

Method assistant

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

Edge cases

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

Common pitfalls

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

Worked example

1.Adım 1 (F1): Step 1: For each criterion j, compute the column minimum x_j^min and maximum x_j^max across all m alternatives. Formül: x_j^{\min} = \min_{i=1}^{m} x_{ij},\quad x_j^{\max} = \max_{i=1}^{m} x_{ij} Anchor: Hwang & Yoon 1981, p.130 (range computation; pending PDF page verification)
2.Adım 2 (F2): Step 2: Apply direction-aware linear rescaling. Benefit criteria: r_ij = (x_ij − x_j^min)/(x_j^max − x_j^min). Cost criteria: r_ij = (x_j^max − x_ij)/(x_j^max − x_j^min). Result: r_ij ∈ [0,1], with 1 always assigned to the best performance and 0 to the worst. Formül: r_{ij} = \begin{cases} \dfrac{x_{ij} - x_j^{\min}}{x_j^{\max} - x_j^{\min}} & j \in J^{+}\text{ (benefit)}\\ \dfrac{x_j^{\max} - x_{ij}}{x_j^{\max} - x_j^{\min}} & j \in J^{-}\text{ (cost)} \end{cases} Anchor: Hwang & Yoon 1981, p.130 Eqs.(4.1a)-(4.1b) (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 minimum x_j^min and maximum x_j^max across all m alternatives. Formül: x_j^{\min} = \min_{i=1}^{m} x_{ij},\quad x_j^{\max} = \max_{i=1}^{m} x_{ij} Anchor: Hwang & Yoon 1981, p.130 (range computation; pending PDF page verification)

2.Adım 2 (F2): Step 2: Apply direction-aware linear rescaling. Benefit criteria: r_ij = (x_ij − x_j^min)/(x_j^max − x_j^min). Cost criteria: r_ij = (x_j^max − x_ij)/(x_j^max − x_j^min). Result: r_ij ∈ [0,1], with 1 always assigned to the best performance and 0 to the worst. Formül: r_{ij} = \begin{cases} \dfrac{x_{ij} - x_j^{\min}}{x_j^{\max} - x_j^{\min}} & j \in J^{+}\text{ (benefit)}\\ \dfrac{x_j^{\max} - x_{ij}}{x_j^{\max} - x_j^{\min}} & j \in J^{-}\text{ (cost)} \end{cases} Anchor: Hwang & Yoon 1981, p.130 Eqs.(4.1a)-(4.1b) (pending PDF page verification)