Grey-MOORA: Grey extension of MOORA

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 MOORA directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

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

Common pitfalls

• •Hatalı: 'GREY-MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Grey numbers/tuples
• •Hatalı: 'GREY-MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'GREY-MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: GREY-MOORA'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: GREY-MOORA'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: Construct grey decision matrix ⊗a_ij=[a_ij^L, a_ij^U]. Normalize per column: ⊗v_ij=[a_ij^L/max_k(a_kj^U), a_ij^U/max_k(a_kj^U)]. Whiten: v̂_ij = ½(v_ij^L + v_ij^U). Vector-normalize whitenised: v̄_ij = v̂_ij / √(Σ_i v̂_ij²). Formül: \otimes v_{ij}=\Bigl[\frac{a_{ij}^L}{\max_k a_{kj}^U},\frac{a_{ij}^U}{\max_k a_{kj}^U}\Bigr];\\ \hat{v}_{ij}=\tfrac{1}{2}(v_{ij}^L+v_{ij}^U);\\ \bar{v}_{ij}=\frac{\hat{v}_{ij}}{\sqrt{\sum_i \hat{v}_{ij}^2}} Anchor: Stanujkic-Magdalinovic-Jovanovic-Stojanovic 2012; Deng 1989 §whitenisation
2. 2.Adım 2 (F2): Step 2: Ratio system score: y_i* = Σ_{j∈Ω_b} w_j·v̄_ij - Σ_{j∈Ω_c} w_j·v̄_ij. Rank descending. Formül: y_i^*=\sum_{j\in\Omega_b}w_j\bar{v}_{ij}-\sum_{j\in\Omega_c}w_j\bar{v}_{ij};\\ \text{rank descending by }y_i^* Anchor: Stanujkic-Magdalinovic-Jovanovic-Stojanovic 2012; Brauers-Zavadskas 2006 §ratio
3. 3.Adım 3 (F3): Step 3 (Optional): Reference point approach: r_j* = max_i(v̄_ij) benefit. y_i** = max_j(w_j·|r_j* - v̄_ij|). Rank ascending. Formül: r_j^*=\max_i\bar{v}_{ij}\;(\text{benefit});\\ y_i^{**}=\max_j\bigl(w_j|r_j^*-\bar{v}_{ij}|\bigr);\\ \text{rank ascending by }y_i^{**} Anchor: Stanujkic-Magdalinovic-Jovanovic-Stojanovic 2012; Brauers-Zavadskas 2006 §ref point

Commonly paired with

• •n_a + GREY-MOORA (common)

How to cite