N-VIKOR - Neutrosophic extension of VIKOR

Overview

n-vikor extends VIKOR 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, lower 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 decision matrix; cost complement.

   $$\mathbf{D}=(⟨T_{ij},I_{ij},F_{ij}⟩{)}_{m\times n};\text{cost: }⟨F_{ij},1-I_{ij},T_{ij}⟩$$

   Bausys & Zavadskas 2015, Sec.2

2. 2

   Best and worst SVN values per criterion.

   $${\tilde{f}}_j^{\ast }=⟨\underset{i}{\max }{T}_{ij},\underset{i}{\min }{I}_{ij},\underset{i}{\min }{F}_{ij}⟩;{\tilde{f}}_j^{-}=⟨\underset{i}{\min }{T}_{ij},\underset{i}{\max }{I}_{ij},\underset{i}{\max }{F}_{ij}⟩$$

   Bausys & Zavadskas 2015, Sec.2 Step2

3. 3

   Normalised neutrosophic gap ratio.

   $$d({\alpha }_1,{\alpha }_2)=\sqrt{\frac{(T_1-T_2{)}^2+(I_1-I_2{)}^2+(F_1-F_2{)}^2}{3}};f_{ij}=\frac{d({\tilde{f}}_j^{\ast },{\tilde{a}}_{ij})}{d({\tilde{f}}_j^{\ast },{\tilde{f}}_j^{-})}$$

   Bausys & Zavadskas 2015, Sec.2 Step3

4. 4

   Utility S_i and regret R_i measures.

   $$S_i=\sum _{j=1}^n{w}_j{f}_{ij};R_i=\underset{j}{\max }{w}_j{f}_{ij}$$

   Bausys & Zavadskas 2015, Sec.2 Step4

5. 5

   Compromise index Q_i; rank ascending. Check acceptability conditions.

   $$Q_i=v\frac{S_i-S^{\ast }}{S^{-}-S^{\ast }}+(1-v)\frac{R_i-R^{\ast }}{R^{-}-R^{\ast }},v=0.5;\text{rank ascending by }{Q}_i$$

   Bausys & Zavadskas 2015, Sec.2 Step5

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

• 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

How to cite