N-AROMAN - Neutrosophic extension of AROMAN

Overview

n-aroman extends AROMAN 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

   Compute SVN score for each rating.

   $$s_{ij}=s({\tilde{a}}_{ij})=\frac{1+T_{ij}-2I_{ij}-F_{ij}}{2}$$

   Bošković et al. 2023, Sec.3 Step1; Biswas 2016 score

2. 2

   Step-1 linear normalisation of SVN scores.

   $$r_{ij}=\{\begin{array}{ll}{s}_{ij}/s_j^{\max }& j\in {\Omega }_b\\ s_j^{\min }/s_{ij}& j\in {\Omega }_c\end{array}$$

   Bošković et al. 2023, Sec.3 Step2

3. 3

   Step-2 vector normalisation of linearly-normalised scores.

   $$z_{ij}=\frac{r_{ij}}{\sqrt{{\sum }_{i=1}^m{r}_{ij}^2}}$$

   Bošković et al. 2023, Sec.3 Step3

4. 4

   Combined two-step normalised value.

   $$t_{ij}=\frac{r_{ij}+z_{ij}}{2}$$

   Bošković et al. 2023, Sec.3 Step4

5. 5

   AROMAN composite score; rank descending.

   $$AROMA{N}_i=\sum _{j=1}^n{w}_j{t}_{ij};\text{rank descending}$$

   Bošković et al. 2023, Sec.3 Step5-6

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