N-MULTIMOORA: Neutrosophic extension of MULTIMOORA

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

Edge cases

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

Common pitfalls

• •Hatalı: 'N-MULTIMOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Hatalı: 'N-MULTIMOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'N-MULTIMOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: N-MULTIMOORA'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: N-MULTIMOORA'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; score + vector normalisation. Formül: \hat{a}_{ij}=\langle F_{ij},1-I_{ij},T_{ij}\rangle\;(j\in\Omega_c);\quad s_{ij}=\tfrac{1+\hat{T}_{ij}-2\hat{I}_{ij}-\hat{F}_{ij}}{2};\quad\bar{s}_{ij}=s_{ij}/\sqrt{\sum_i s_{ij}^2} Anchor: Stanujkic et al. 2017, Sec.3 Step1
2. 2.Adım 2 (F2): Sub-method 1: Ratio System score. Formül: y_i^{\mathrm{RS}}=\sum_{j=1}^n w_j\bar{s}_{ij};\quad\text{rank descending} Anchor: Stanujkic et al. 2017, Sec.3 RS
3. 3.Adım 3 (F3): Sub-method 2: Reference Point Chebyshev score. Formül: r_j^*=\max_i\bar{s}_{ij};\quad y_i^{\mathrm{RP}}=\max_j\;w_j|r_j^*-\bar{s}_{ij}|;\quad\text{rank ascending} Anchor: Stanujkic et al. 2017, Sec.3 RP
4. 4.Adım 4 (F4): Sub-method 3: Full Multiplicative Form via SVNWG operator. Formül: \tilde{U}_i=\mathrm{SVNWG}_w(\hat{a}_{i1},\ldots,\hat{a}_{in})=\Bigl\langle\prod_j\hat{T}_{ij}^{w_j},\;1-\prod_j(1-\hat{I}_{ij})^{w_j},\;1-\prod_j(1-\hat{F}_{ij})^{w_j}\Bigr\rangle;\quad y_i^{\mathrm{FMF}}=s(\tilde{U}_i);\quad\text{rank descending} Anchor: Stanujkic et al. 2017, Sec.3 FMF; Ye 2014 SVNWG
5. 5.Adım 5 (F5): Theory of Dominance: final rank from pairwise dominance across RS, RP, FMF. Formül: A_i\succ A_k\iff A_i\text{ ranks better in }\geq 2\text{ of }\{RS,RP,FMF\};\quad\text{count dominances for final order} Anchor: Brauers & Zavadskas 2010; Stanujkic et al. 2017, Sec.3 Dominance

Commonly paired with

• •n_a + N-MULTIMOORA (common)

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