L2T-EDAS - 2-Demetli Dilsel Nötrosofik EDAS

Formül adımları

Analiz motorunun yöntem bildirimindeki (manifest F.steps) adımlar; raporlardaki formüllerle aynı kaynaktır.

1. Adım 1 — Her karar vericinin R^r = [φ^r_ij]_{m×n} değerlendirme matrislerini topla; her φ^r_ij: 2-demetli dilsel nötrosofik sayı (2TLNS).

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

   \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

2. Adım 2 — Maliyet kriterler için tamamlayıcı alınır: φ'^r_ij = (φ^r_ij)^c.

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

   \varphi'^r_{ij}=\begin{cases}(\varphi^r_{ij})^c & c_j\text{ cost}\\\varphi^r_{ij} & c_j\text{ benefit}\end{cases}

3. Adım 3 — Karar verici görüşlerini 2TLNNHWA ile v_r ağırlıklarıyla birleştir.

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

   \varphi'_{ij}=2\text{TLNNHWA}(\varphi'^1_{ij},\ldots,\varphi'^h_{ij})=\bigoplus_{r=1}^h v_r\varphi'^r_{ij}

4. Adım 4 — Her kriter için Ortalama Çözüm AV_j hesaplanır.

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

   AV_j=2\text{TLNNHWA}(\varphi'_{1j},\ldots,\varphi'_{mj})\text{ with weights }(1/m,\ldots,1/m)

5. Adım 5 — Ortalamadan Pozitif Uzaklık (PDA) ve Negatif Uzaklık (NDA) hesaplanır.

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

   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)}

6. Adım 6 — Ağırlıklı toplamlar SP_i ve SN_i; normalize; Değerlendirme Skoru AS_i = (NSP_i+NSN_i)/2; azalan sırala.

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

   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}

Sezgi

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

Sonucu okuma: 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.

Varsayımlar

• 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

Ne zaman kullanılmaz

• Classical data sufficient - use base EDAS directly (avoid unnecessary uncertainty layer)
• Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sınırlılıklar

• 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

Sık yapılan hatalar

• Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin 2TL: s_i ∈ S (linguistic term set), α ∈ [-0.5,0.5) koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: Δ^{-1}(s_i, α) = i + α kanonik seçimdir.