N-CODAS: Neutrosophic extension of CODAS

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

Edge cases

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

Common pitfalls

• •Hatalı: 'N-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Hatalı: 'N-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'N-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: N-CODAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: N-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): SVN matrix; cost normalisation via complement. Formül: \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle);\quad\text{cost: }\hat{a}_{ij}=\langle F_{ij},1-I_{ij},T_{ij}\rangle;\quad\text{benefit: }\hat{a}_{ij}=\tilde{a}_{ij} Anchor: Yüksel 2020, Sec.3 Step1-2
2. 2.Adım 2 (F2): Weighted normalised SVNNs. Formül: \tilde{v}_{ij}=\langle 1-(1-\hat{T}_{ij})^{w_j},\;\hat{I}_{ij}^{w_j},\;\hat{F}_{ij}^{w_j}\rangle Anchor: Yüksel 2020, Sec.3 Step3
3. 3.Adım 3 (F3): Neutrosophic Negative Ideal Solution. Formül: \alpha_j^-=\langle\min_i T_{ij}^v,\;\max_i I_{ij}^v,\;\max_i F_{ij}^v\rangle Anchor: Yüksel 2020, Sec.3 Step4
4. 4.Adım 4 (F4): Euclidean E_i and Taxicab T_i separations from NIS. Formül: d_E(\alpha_1,\alpha_2)=\sqrt{\tfrac{(T_1-T_2)^2+(I_1-I_2)^2+(F_1-F_2)^2}{3}};\quad d_H=\tfrac{|T_1-T_2|+|I_1-I_2|+|F_1-F_2|}{3};\quad E_i=\sqrt{\sum_j w_j[d_E(\tilde{v}_{ij},\alpha_j^-)]^2};\quad T_i=\sum_j w_j d_H(\tilde{v}_{ij},\alpha_j^-) Anchor: Yüksel 2020, Sec.3 Step5
5. 5.Adım 5 (F5): Relative assessment matrix h_ik with threshold τ. Formül: h_{ik}=(E_i-E_k)+\psi(E_i-E_k)\cdot(T_i-T_k);\quad\psi(x)=\begin{cases}1&|x|\geq\tau\\0&|x|<\tau\end{cases},\;\tau=0.02 Anchor: Yüksel 2020, Sec.3 Step6
6. 6.Adım 6 (F6): Appraisal score AS_i; rank descending. Formül: AS_i=\sum_{k=1}^m h_{ik};\quad\text{rank descending} Anchor: Yüksel 2020, Sec.3 Step7-8

Commonly paired with

• •n_a + N-CODAS (common)

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