N-VIKOR: Neutrosophic extension of VIKOR

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

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

Edge cases

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

Common pitfalls

• •Hatalı: 'N-VIKOR bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Hatalı: 'N-VIKOR bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'N-VIKOR bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: N-VIKOR'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: N-VIKOR'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 decision matrix; cost complement. Formül: \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle)_{m\times n};\quad\text{cost: }\langle F_{ij},1-I_{ij},T_{ij}\rangle Anchor: Bausys & Zavadskas 2015, Sec.2
2. 2.Adım 2 (F2): Best and worst SVN values per criterion. Formül: \tilde{f}_j^*=\langle\max_i T_{ij},\min_i I_{ij},\min_i F_{ij}\rangle;\quad\tilde{f}_j^-=\langle\min_i T_{ij},\max_i I_{ij},\max_i F_{ij}\rangle Anchor: Bausys & Zavadskas 2015, Sec.2 Step2
3. 3.Adım 3 (F3): Normalised neutrosophic gap ratio. Formül: d(\alpha_1,\alpha_2)=\sqrt{\tfrac{(T_1-T_2)^2+(I_1-I_2)^2+(F_1-F_2)^2}{3}};\quad f_{ij}=\frac{d(\tilde{f}_j^*,\tilde{a}_{ij})}{d(\tilde{f}_j^*,\tilde{f}_j^-)} Anchor: Bausys & Zavadskas 2015, Sec.2 Step3
4. 4.Adım 4 (F4): Utility S_i and regret R_i measures. Formül: S_i=\sum_{j=1}^n w_j f_{ij};\quad R_i=\max_j\;w_j f_{ij} Anchor: Bausys & Zavadskas 2015, Sec.2 Step4
5. 5.Adım 5 (F5): Compromise index Q_i; rank ascending. Check acceptability conditions. Formül: Q_i=v\frac{S_i-S^*}{S^--S^*}+(1-v)\frac{R_i-R^*}{R^--R^*},\;v=0.5;\quad\text{rank ascending by }Q_i Anchor: Bausys & Zavadskas 2015, Sec.2 Step5

Commonly paired with

• •n_a + N-VIKOR (common)

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