MPSI: Modified PSI method for objective weighting (Modified Preference Selection Index weighting)

Overview

Modified PSI variance-based objective weighting (weight extraction from PSI preference variation). Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Modified PSI variance-based objective weighting (weight extraction from PSI preference variation)

Limitations

• •Assumes: Decision matrix exists with measurable criteria
• •Assumes: Sufficient inter-alternative variation per criterion

Assumptions to verify

• •Decision matrix exists with measurable criteria
• •Sufficient inter-alternative variation per criterion

When not to use

• •No data variation (constant criterion) → weight degenerates
• •Expert judgment is the actual driver → use subjective weighting

Edge cases

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

Common pitfalls

• •Hatalı: 'MPSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix exists with measurable criteria
• •Hatalı: 'MPSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Sufficient inter-alternative variation per criterion
• •Hatalı: MPSI'yi 'No data variation (constant criterion) → weight degenerates' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: MPSI'yi 'Expert judgment is the actual driver → use subjective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Linear-max normalisation: for benefit x_ij / max_k(x_kj); for cost min_k(x_kj) / x_ij. Formül: \bar{x}_{ij} = \frac{x_{ij}}{\max_k x_{kj}} \text{ (benefit)};\quad \bar{x}_{ij} = \frac{\min_k x_{kj}}{x_{ij}} \text{ (cost)} Anchor: Maniya & Bhatt 2010, p.1786 Eqs.(1)-(2)
2. 2.Adım 2 (F2): Step 2: Compute mean x̄_j and Preference Variation Value Φ_j = Σ_i (x̄_ij − x̄_j)² for each criterion. Formül: \bar{x}_j = \frac{1}{m}\sum_i \bar{x}_{ij};\quad \Phi_j = \sum_i (\bar{x}_{ij} - \bar{x}_j)^2 Anchor: Maniya & Bhatt 2010, p.1786 Eqs.(3)-(4)
3. 3.Adım 3 (F3): Step 3: Compute weights from deviation from maximum variance: Ω_j = (1 − Φ_j) / Σ_k (1 − Φ_k). This is the MPSI weight extraction (distinct from PSI's I_i which ranks alternatives). Formül: \Omega_j = \frac{1-\Phi_j}{\sum_k (1-\Phi_k)} Anchor: Maniya & Bhatt 2010, p.1786 Eq.(5)

Commonly paired with

• •MPSI + TOPSIS (high)
• •MPSI + VIKOR (high)
• •MPSI + EDAS (high)
• •MPSI + WASPAS (high)
• •MPSI + MARCOS (high)

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