L2T-COPRAS: Linguistic extension of L2T-COPRAS

Overview

Linguistic outranking/ranking: 2-Tuple Linguistic Variable (2TL: (s_i, α)). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Linguistic outranking/ranking: 2-Tuple Linguistic Variable (2TL: (s_i, α))
• •Preserves linguistic_2tuple 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 Linguistic 2-Tuple 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 Linguistic 2-Tuple 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 COPRAS directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

• •See F.steps and D.parameters for L2T-COPRAS-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'L2T-COPRAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Linguistic 2-Tuple numbers/tuples
• •Hatalı: 'L2T-COPRAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'L2T-COPRAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: L2T-COPRAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: L2T-COPRAS'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 the 2-tuple linguistic decision matrix x̃_ij = (s_ij, α_ij) on linguistic term set S={s_0,…,s_q} with Δ⁻¹(s_i,α)=i+α; define criterion weights w_j and direction sets Ω_max (benefit) and Ω_min (cost). Formül: \tilde{D} = [(s_{ij}, \alpha_{ij})]_{m\times n};\ \Delta^{-1}(s_{i}, \alpha) = i + \alpha;\ \Omega_{max}\cup\Omega_{min} = \{1,\dots,n\} Anchor: Report §3.5 Step 1; Gai 2021 ITL-COPRAS
2. 2.Adım 2 (F2): Step 2: Weighted 2-tuple decision matrix d̃_ij = Δ(w_j · Δ⁻¹(s_ij,α_ij)) using 2-tuple weighted-aggregation arithmetic. Formül: \tilde{d}_{ij} = \Delta\!\left(w_{j}\cdot \Delta^{-1}(s_{ij},\alpha_{ij})\right) Anchor: Report §3.5 Step 1: weighted normalised matrix
3. 3.Adım 3 (F3): Step 3: Sum of benefit P_i = Σ_{j ∈ Ω_max} Δ⁻¹(d̃_ij) and sum of cost R_i = Σ_{j ∈ Ω_min} Δ⁻¹(d̃_ij). Formül: P_{i} = \sum_{j \in \Omega_{max}} \Delta^{-1}(\tilde{d}_{ij}),\quad R_{i} = \sum_{j \in \Omega_{min}} \Delta^{-1}(\tilde{d}_{ij}) Anchor: Report §3.5 Formulas 2-3: sum of benefit/cost criteria
4. 4.Adım 4 (F4): Step 4: Relative significance Q_i = P_i + (Σ_k R_k)/(R_i · Σ_k 1/R_k) combining benefit and cost terms. Formül: Q_{i} = P_{i} + \dfrac{\sum_{k=1}^{m} R_{k}}{R_{i}\cdot \sum_{k=1}^{m} \dfrac{1}{R_{k}}} Anchor: Report §3.5 Formula 4: relative significance
5. 5.Adım 5 (F5): Step 5: Utility degree N_i = (Q_i / max_k Q_k) × 100% with descending ranking. Formül: N_{i} = \dfrac{Q_{i}}{\max_{k} Q_{k}} \times 100\%;\ \ \text{rank} = \text{argsort}_{\text{desc}}(N_{i}) Anchor: Report §3.5: utility degree and ranking

Commonly paired with

• •n_a + L2T-COPRAS (common)

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