N-WPM - Neutrosophic extension of WPM

Overview

n-wpm extends WPM to handle Neutrosophic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3) algebra. The final scores are defuzzified via score function S = (T − F + 1)/2 before ranking.

Output

utility, higher is better

Data

Single-Valued Neutrosophic, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Single-Valued Neutrosophic MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

How it works

1. 1

   SVN matrix; cost complement for cost criteria.

   $$\mathbf{D}=(⟨T_{ij},I_{ij},F_{ij}⟩);\text{cost: }{\hat{a}}_{ij}=⟨F_{ij},1-I_{ij},T_{ij}⟩;\text{benefit: }{\hat{a}}_{ij}={\tilde{a}}_{ij}$$

   Ye 2014, Sec.3; Miller & Starr 1969

2. 2

   SVNWG operator: neutrosophic weighted geometric product.

   $${\tilde{P}}_i={\mathrm{SVNWG}}_w({\hat{a}}_{i1},\dots ,{\hat{a}}_{in})=⟨\prod _{j=1}^n{\hat{T}}_{ij}^{w_j},1-\prod _{j=1}^n(1-{\hat{I}}_{ij}{)}^{w_j},1-\prod _{j=1}^n(1-{\hat{F}}_{ij}{)}^{w_j}⟩$$

   Ye 2014, Def.5 SVNWG

3. 3

   Score and rank descending; tiebreaker accuracy a(α)=T-F.

   $$s_i=\frac{1+{\tilde{T}}_i^P-2{\tilde{I}}_i^P-{\tilde{F}}_i^P}{2};a_i={\tilde{T}}_i^P-{\tilde{F}}_i^P;\text{rank descending by }{s}_i$$

   Ye 2014, Sec.3

Fits when / Look elsewhere when

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

Edge cases and pitfalls

• •tiebreaker accuracy a(α)=T-F.

• Value-space violation: ensure all entries satisfy SVNS: T,I,F ∈ [0,1]; 0 ≤ T+I+F ≤ 3 before computation.

• Defuzzification method affects ranking: score function S = (T − F + 1)/2 is the canonical choice but alternatives exist.

Works with

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