WAM: Weighted Arithmetic Mean

Overview

Linear additive aggregation operator. Output typically rank_position (lower value = preferred).

Strengths

• •Method-specific: Linear additive aggregation operator

Limitations

• •Assumes: Input is a rank matrix (1=best, m=worst per voter)
• •Assumes: Each voter ranks all alternatives

Assumptions to verify

• •Input is a rank matrix (1=best, m=worst per voter)
• •Each voter ranks all alternatives

When not to use

• •Cardinal preferences important → use a MAUT method

Edge cases

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

Common pitfalls

• •Hatalı: 'WAM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Input is a rank matrix (1=best, m=worst per voter)
• •Hatalı: 'WAM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Each voter ranks all alternatives
• •Hatalı: WAM'yi 'Cardinal preferences important → use a MAUT method' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Validate weights satisfy Σw_j = 1 and w_j ≥ 0. Formül: \sum_{j=1}^{n} w_{j} = 1,\quad w_{j}\ge 0 Anchor: Yager 1988, p.184 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Weighted arithmetic mean WAM(x_1,…,x_n) = Σ w_j x_j. Formül: \text{WAM}(x_{1},\ldots,x_{n}) = \sum_{j=1}^{n} w_{j}\,x_{j} Anchor: Yager 1988, p.184 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Apply WAM per alternative; descending ranking. Formül: S_{i} = \sum_{j=1}^{n} w_{j}\,x_{ij},\quad i=1,\ldots,m Anchor: Yager 1988, p.185 Eq.(3)

How to cite