N-TODIM: Neutrosophic extension of TODIM

Overview

Neutrosophic outranking/ranking: Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Neutrosophic outranking/ranking: Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3)
• •Preserves single_valued_neutrosophic 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 Single-Valued Neutrosophic 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 Single-Valued Neutrosophic 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 TODIM directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

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

Common pitfalls

• •Hatalı: 'N-TODIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Hatalı: 'N-TODIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'N-TODIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: N-TODIM'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: N-TODIM'yi 'Aggregation operator (PFWA/PFOWA/etc.) not specified' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): SVN matrix; cost complement. Formül: \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle);\quad\text{cost: }\tilde{a}_{ij}^c=\langle F_{ij},1-I_{ij},T_{ij}\rangle Anchor: Ji et al. 2018, Sec.3 Step1
2. 2.Adım 2 (F2): Relative criterion weights; reference criterion w_r = max w_j. Formül: \bar{w}_{jr}=w_j/w_r,\quad w_r=\max_j w_j Anchor: Gomes & Lima 1992, Eq.(2); Ji et al. 2018, Sec.3 Step2
3. 3.Adım 3 (F3): Dominance contribution: gain (√) and loss (−1/θ·√) with neutrosophic distance. Formül: d_j(i,k)=d(\tilde{a}_{ij},\tilde{a}_{kj})=\sqrt{\tfrac{(T_{ij}-T_{kj})^2+(I_{ij}-I_{kj})^2+(F_{ij}-F_{kj})^2}{3}};\quad\phi_j(A_i,A_k)=\begin{cases}+\sqrt{\bar{w}_{jr}d_j/\sum_j\bar{w}_{jr}}&s_{ij}>s_{kj}\\0&s_{ij}=s_{kj}\\-\tfrac{1}{\theta}\sqrt{(\sum_j\bar{w}_{jr})\cdot d_j/\bar{w}_{jr}}&s_{ij}<s_{kj}\end{cases} Anchor: Ji et al. 2018, Sec.3 Step3; θ=1 default
4. 4.Adım 4 (F4): Overall dominance δ(A_i,A_k) summed over criteria. Formül: \delta(A_i,A_k)=\sum_{j=1}^n\phi_j(A_i,A_k) Anchor: Ji et al. 2018, Sec.3 Step4
5. 5.Adım 5 (F5): Global normalised value ξ_i; rank descending. Formül: \xi_i=\frac{\sum_k\delta(A_i,A_k)-\min_k\sum_t\delta(A_k,A_t)}{\max_k\sum_t\delta(A_k,A_t)-\min_k\sum_t\delta(A_k,A_t)};\quad\text{rank descending} Anchor: Ji et al. 2018, Sec.3 Step5-6

Commonly paired with

• •n_a + N-TODIM (common)

How to cite