N-WPM: Neutrosophic extension of WPM

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

Edge cases

• •tiebreaker accuracy a(α)=T-F.

Common pitfalls

• •Hatalı: 'N-WPM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Hatalı: 'N-WPM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'N-WPM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: N-WPM'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: N-WPM'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 for cost criteria. 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: Ye 2014, Sec.3; Miller & Starr 1969
2. 2.Adım 2 (F2): SVNWG operator: neutrosophic weighted geometric product. Formül: \tilde{P}_i=\mathrm{SVNWG}_w(\hat{a}_{i1},\ldots,\hat{a}_{in})=\Bigl\langle\prod_{j=1}^n\hat{T}_{ij}^{w_j},\;1-\prod_{j=1}^n(1-\hat{I}_{ij})^{w_j},\;1-\prod_{j=1}^n(1-\hat{F}_{ij})^{w_j}\Bigr\rangle Anchor: Ye 2014, Def.5 SVNWG
3. 3.Adım 3 (F3): Score and rank descending; tiebreaker accuracy a(α)=T-F. Formül: s_i=\tfrac{1+\tilde{T}_i^P-2\tilde{I}_i^P-\tilde{F}_i^P}{2};\quad a_i=\tilde{T}_i^P-\tilde{F}_i^P;\quad\text{rank descending by }s_i Anchor: Ye 2014, Sec.3

Commonly paired with

• •n_a + N-WPM (common)

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