L2T-EDAS: 2-Tuple Linguistic Neutrosophic EDAS

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

Edge cases

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

Common pitfalls

• •Hatalı: 'L2T-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Linguistic 2-Tuple numbers/tuples
• •Hatalı: 'L2T-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'L2T-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: L2T-EDAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: L2T-EDAS'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: Collect evaluation matrices R^r = [φ^r_ij]_{m×n} from each of r=1..h decision makers where each φ^r_ij is a 2-tuple linguistic neutrosophic number (2TLNN): 〈(s_t,α),(s_i,β),(s_f,χ)〉 with s_t,s_i,s_f ∈ S = {s_0,...,s_k}. Formül: \varphi^r_{ij}=\langle(s_t,\alpha),(s_i,\beta),(s_f,\chi)\rangle,\quad 0\le\Delta^{-1}(s_t,\alpha)+\Delta^{-1}(s_i,\beta)+\Delta^{-1}(s_f,\chi)\le 3k Anchor: p.1 Eq.(16)
2. 2.Adım 2 (F2): Step 2: Normalize for cost criteria by taking complement: φ'^r_ij = (φ^r_ij)^c = 〈(s_f,χ),(s_i,β),(s_t,α)〉 for cost; φ'^r_ij = φ^r_ij for benefit. Formül: \varphi'^r_{ij}=\begin{cases}(\varphi^r_{ij})^c & c_j\text{ cost}\\\varphi^r_{ij} & c_j\text{ benefit}\end{cases} Anchor: p.6 Eq.(18)
3. 3.Adım 3 (F3): Step 3: Aggregate DM opinions using 2TLNNHWA operator with DM weights v_r: φ'_ij = 2TLNNHWA(φ'^1_ij,...,φ'^h_ij) = ⊕^h_{r=1} v_r φ'^r_ij. Formül: \varphi'_{ij}=2\text{TLNNHWA}(\varphi'^1_{ij},\ldots,\varphi'^h_{ij})=\bigoplus_{r=1}^h v_r\varphi'^r_{ij} Anchor: p.5 Eq.(13)
4. 4.Adım 4 (F4): Step 4: Compute Average Solution AV_j for each criterion j by aggregating all alternatives' fused values using 2TLNNHWA with equal weights (1/m). Formül: AV_j=2\text{TLNNHWA}(\varphi'_{1j},\ldots,\varphi'_{mj})\text{ with weights }(1/m,\ldots,1/m) Anchor: p.6 Eq.(19)
5. 5.Adım 5 (F5): Step 5: Positive Distance from Average (PDA_ij) and Negative Distance from Average (NDA_ij): based on score comparison s(φ'_ij) vs s(AV_j); PDA_ij = max(0, s(φ'_ij)-s(AV_j)) / s(AV_j); NDA_ij = max(0, s(AV_j)-s(φ'_ij)) / s(AV_j). Formül: PDA_{ij}=\frac{\max(0,s(\varphi'_{ij})-s(AV_j))}{s(AV_j)},\quad NDA_{ij}=\frac{\max(0,s(AV_j)-s(\varphi'_{ij}))}{s(AV_j)} Anchor: p.6 Eqs.(26-27)
6. 6.Adım 6 (F6): Step 6: Compute weighted sums SP_i = Σ_j ω_j PDA_ij and SN_i = Σ_j ω_j NDA_ij; normalize: NSP_i = SP_i/max_i(SP_i), NSN_i = 1 - SN_i/max_i(SN_i); compute Appraisal Score AS_i = (NSP_i + NSN_i)/2; rank descending. Formül: SP_i=\sum_j\omega_j PDA_{ij},\quad SN_i=\sum_j\omega_j NDA_{ij},\quad AS_i=\frac{NSP_i+NSN_i}{2} Anchor: p.6 Eqs.(28-32)

Commonly paired with

• •n_a + L2T-EDAS (common)

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