L2T-EDAS - 2-Tuple Linguistic Neutrosophic EDAS

Overview

l2t-edas extends L2T-EDAS to handle Linguistic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using 2-Tuple Linguistic Variable (2TL: (s_i, α)) algebra. The final scores are defuzzified via Δ^{-1}(s_i, α) = i + α before ranking.

Output

utility, higher is better

Data

Linguistic Neutrosophic, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Linguistic 2-Tuple MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

How it works

1. 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}.

   $${\phi }_{ij}^r=⟨(s_t,\alpha ),(s_i,\beta ),(s_f,\chi )⟩,0\le {\Delta }^{-1}(s_t,\alpha )+{\Delta }^{-1}(s_i,\beta )+{\Delta }^{-1}(s_f,\chi )\le 3k$$

   p.1 Eq.(16)

2. 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.

   $${\phi }_{ij}^{\prime r}=\{\begin{array}{ll}({\phi }_{ij}^r{)}^c& c_j\text{ cost}\\ {\phi }_{ij}^r& c_j\text{ benefit}\end{array}$$

   p.6 Eq.(18)

3. 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.

   $${\phi }_{ij}^{\prime }=2\text{TLNNHWA}({\phi }_{ij}^{\prime 1},\dots ,{\phi }_{ij}^{\prime h})=\underset{r=1}{\overset{h}{⨁}}{v}_r{\phi }_{ij}^{\prime r}$$

   p.5 Eq.(13)

4. 4

   Compute Average Solution AV_j for each criterion j by aggregating all alternatives' fused values using 2TLNNHWA with equal weights (1/m).

   $$A{V}_j=2\text{TLNNHWA}({\phi }_{1j}^{\prime },\dots ,{\phi }_{mj}^{\prime })\text{ with weights }(1/m,\dots ,1/m)$$

   p.6 Eq.(19)

5. 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).

   $$PD{A}_{ij}=\frac{\max (0,s({\phi }_{ij}^{\prime })-s(A{V}_j))}{s(A{V}_j)},ND{A}_{ij}=\frac{\max (0,s(A{V}_j)-s({\phi }_{ij}^{\prime }))}{s(A{V}_j)}$$

   p.6 Eqs.(26-27)

6. 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.

   $$S{P}_i=\sum _j{\omega }_{j}PD{A}_{ij},S{N}_i=\sum _j{\omega }_{j}ND{A}_{ij},A{S}_i=\frac{NS{P}_i+NS{N}_i}{2}$$

   p.6 Eqs.(28-32)

Fits when / Look elsewhere when

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

Edge cases and pitfalls

• Value-space violation: ensure all entries satisfy 2TL: s_i ∈ S (linguistic term set), α ∈ [-0.5,0.5) before computation.

• Defuzzification method affects ranking: Δ^{-1}(s_i, α) = i + α is the canonical choice but alternatives exist.

Works with

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