Grey-WASPAS: Grey extension of WASPAS

Overview

Grey outranking/ranking: Grey Interval Number (GIN: [x̲, x̄]). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Grey outranking/ranking: Grey Interval Number (GIN: [x̲, x̄])
• •Preserves grey uncertainty through the pipeline rather than premature crispification at elicitation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Rank reversal known on alternative-set changes (ref: inherited from crisp base; cf. Belton-Gear 1983, Wang-Luo 2009)
• •Assumes: Decision matrix entries are valid Grey numbers/tuples
• •Assumes: Underlying crisp method's compensation assumption holds in uncertain space
• •Assumes: All decision-maker(s) and experts use the same linguistic/uncertainty scale

Assumptions to verify

• •Decision matrix entries are valid Grey numbers/tuples
• •Underlying crisp method's compensation assumption holds in uncertain space
• •All decision-maker(s) and experts use the same linguistic/uncertainty scale

When not to use

• •Crisp data sufficient: use base WASPAS directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

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

Common pitfalls

• •Hatalı: 'GREY-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Grey numbers/tuples
• •Hatalı: 'GREY-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'GREY-WASPAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: GREY-WASPAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: GREY-WASPAS'yi 'Aggregation operator (PFWA/PFOWA/etc.) not specified' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Normalize grey matrix (benefit/cost); whiten: v̂_ij=½(v_ij^L+v_ij^U). Formül: \hat{v}_{ij}=\tfrac{1}{2}\bigl(v_{ij}^{L,\mathrm{norm}}+v_{ij}^{U,\mathrm{norm}}\bigr) Anchor: Zavadskas-Turskis 2012; Deng 1989
2. 2.Adım 2 (F2): Step 2: WSM score: Q_i^(1) = Σ_j w_j·v̂_ij. Formül: Q_i^{(1)}=\sum_j w_j\hat{v}_{ij} Anchor: Zavadskas-Turskis 2012 §WSM
3. 3.Adım 3 (F3): Step 3: WPM score: Q_i^(2) = Π_j v̂_ij^(w_j). Formül: Q_i^{(2)}=\prod_j\hat{v}_{ij}^{w_j} Anchor: Zavadskas-Turskis 2012 §WPM
4. 4.Adım 4 (F4): Step 4: Combined: Q_i = λ·Q_i^(1) + (1-λ)·Q_i^(2), λ=0.5. Rank descending. Formül: Q_i=\lambda Q_i^{(1)}+(1-\lambda)Q_i^{(2)},\quad\lambda=0.5;\\ \text{rank descending} Anchor: Zavadskas-Turskis 2012 §combined WASPAS

Commonly paired with

• •n_a + GREY-WASPAS (common)

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