N-RAFSI - Neutrosophic extension of RAFSI

Overview

n-rafsi extends RAFSI 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 score extraction.

   $$s_{ij}=\frac{1+T_{ij}-2I_{ij}-F_{ij}}{2}$$

   Žižović et al. 2020, Sec.2; SVN score Ye 2014

2. 2

   Ideal and non-ideal scores per criterion.

   $$s_j^{\mathrm{id}}=\{\begin{array}{ll}{\max }_i{s}_{ij}& j\in {\Omega }_b\\ {\min }_i{s}_{ij}& j\in {\Omega }_c\end{array};s_j^{\mathrm{nid}}=\{\begin{array}{ll}{\min }_i{s}_{ij}& j\in {\Omega }_b\\ {\max }_i{s}_{ij}& j\in {\Omega }_c\end{array}$$

   Žižović et al. 2020, Sec.2 Step2

3. 3

   Map scores to [1, n_CI] interval.

   $${\hat{x}}_{ij}=1+(n_{\mathrm{CI}}-1)\cdot \frac{|s_{ij}-s_j^{\mathrm{nid}}|}{|s_j^{\mathrm{id}}-s_j^{\mathrm{nid}}|},n_{\mathrm{CI}}\text{ user-defined}$$

   Žižović et al. 2020, Sec.2 Step3

4. 4

   RAFSI composite score.

   $$R_i=\sum _{j=1}^n{w}_j\frac{{\hat{x}}_{ij}}{n_{\mathrm{CI}}}$$

   Žižović et al. 2020, Sec.2 Step4

5. 5

   Rank descending by R_i.

   $$\text{rank descending by }{R}_i$$

   Žižović et al. 2020, 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.

• If extras.ideal_points/anti_ideal_points are not supplied, the anchors are derived from the observed data and the RAFSI rank-reversal-free guarantee does NOT hold: scores of existing alternatives can shift when an alternative is added or removed. Declare fixed anchors to keep the guarantee.

Works with

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