PSI: Preference Selection Index

Overview

Preference variation index (weight-free statistical). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Preference variation index (weight-free statistical)

Limitations

• •Assumes: Criteria preferences are independent (no synergistic interactions)
• •Assumes: Compensation is acceptable: high score on one criterion can offset low on another
• •Assumes: Decision matrix is complete (no missing values)

Assumptions to verify

• •Criteria preferences are independent (no synergistic interactions)
• •Compensation is acceptable: high score on one criterion can offset low on another
• •Decision matrix is complete (no missing values)

When not to use

• •Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• •Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Edge cases

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

Common pitfalls

• •Hatalı: 'PSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'PSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'PSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: PSI'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: PSI'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Linear normalisation per criterion direction. Formül: r_{ij} = \begin{cases} x_{ij}/\max_{i} x_{ij} & j\in J^{+} \\ \min_{i} x_{ij}/x_{ij} & j\in J^{-} \end{cases} Anchor: Maniya-Bhatt 2010, p.1631 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Column means r̄_j and squared deviations Σ (r_ij − r̄_j)². Formül: \bar{r}_{j} = \tfrac{1}{m}\sum_{i} r_{ij},\quad V_{j} = \sum_{i=1}^{m}(r_{ij}-\bar{r}_{j})^{2} Anchor: Maniya-Bhatt 2010, p.1631 Eq.(3)
3. 3.Adım 3 (F3): Step 3: Preference variation φ_j = 1 − V_j and self-derived weights w_j = φ_j / Σ φ_k. Formül: \phi_{j} = 1 - V_{j},\quad w_{j} = \dfrac{\phi_{j}}{\sum_{k=1}^{n} \phi_{k}} Anchor: Maniya-Bhatt 2010, p.1632 Eqs.(4)-(5)
4. 4.Adım 4 (F4): Step 4: Preference Selection Index I_i = Σ w_j r_ij and descending ranking. Formül: I_{i} = \sum_{j=1}^{n} w_{j}\,r_{ij} Anchor: Maniya-Bhatt 2010, p.1632 Eq.(6)

Commonly paired with

• •AHP + PSI (high)
• •BWM + PSI (high)
• •ENTROPY + PSI (high)
• •CRITIC + PSI (high)
• •SWARA + PSI (high)

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