L2T-CODAS: Linguistic extension of L2T-CODAS

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

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

Edge cases

• •when Euclidean gap is significant.

Common pitfalls

• •Hatalı: 'L2T-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Linguistic 2-Tuple numbers/tuples
• •Hatalı: 'L2T-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'L2T-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: L2T-CODAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: L2T-CODAS'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}; define criteria weights w_j and direction sets J^+ (benefit) / J^- (cost). Δ⁻¹(s_i,α)=i+α is the canonical defuzzification. Formül: \tilde{D} = [(s_{ij}, \alpha_{ij})]_{m\times n};\ \Delta^{-1}(s_{i}, \alpha) = i + \alpha;\ J^{+}\cup J^{-} = \{1,\dots,n\} Anchor: Report §3.4 Step 1; He 2019 P2TL-CODAS
2. 2.Adım 2 (F2): Step 2: Negative-Ideal Solution per criterion in 2-tuple space: (s_j^-, α_j^-) = min_i (s_ij, α_ij) for benefit criteria (max_i for cost), with the min/max taken in the Δ⁻¹ order. Formül: (s_{j}^{-}, \alpha_{j}^{-}) = \begin{cases}\min_{i}(s_{ij},\alpha_{ij}) & j\in J^{+}\\ \max_{i}(s_{ij},\alpha_{ij}) & j\in J^{-}\end{cases} Anchor: Report §3.4 Formula 1: negative ideal solution
3. 3.Adım 3 (F3): Step 3: Euclidean distance E_i and Taxicab distance T_i from the 2-tuple negative-ideal, using 2-tuple distance d((s_ij,α_ij),(s_j^-,α_j^-)) = |Δ⁻¹(s_ij,α_ij) − Δ⁻¹(s_j^-,α_j^-)| with criterion weights w_j. Formül: E_{i} = \sqrt{\sum_{j=1}^{n} w_{j}\, d^{2}((s_{ij},\alpha_{ij}),(s_{j}^{-},\alpha_{j}^{-}))},\ \ T_{i} = \sum_{j=1}^{n} w_{j}\, d((s_{ij},\alpha_{ij}),(s_{j}^{-},\alpha_{j}^{-})) Anchor: Report §3.4 Formulas 2-3: Euclidean and Taxicab distances
4. 4.Adım 4 (F4): Step 4: Relative assessment matrix h_ik via threshold ψ(τ) on |E_i − E_k|; combines Euclidean and Taxicab gaps when Euclidean gap is significant. Formül: h_{ik} = (E_{i}-E_{k}) + \psi(E_{i}-E_{k})\cdot(T_{i}-T_{k}),\ \ \psi(z) = \begin{cases}1 & |z|\ge\tau\\ 0 & |z|<\tau\end{cases} Anchor: Report §3.4: relative assessment matrix
5. 5.Adım 5 (F5): Step 5: Final assessment score H_i = E_i + ψ·E_i·T_i (combined-distance form), or equivalently H_i = Σ_k h_ik; rank in descending order. Formül: H_{i} = E_{i} + \psi\cdot E_{i}\cdot T_{i} = \sum_{k=1}^{m} h_{ik};\ \ \text{rank} = \text{argsort}_{\text{desc}}(H_{i}) Anchor: Report §3.4 Formula 4: assessment score

Commonly paired with

• •n_a + L2T-CODAS (common)

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