N-EDAS - Neutrosophic extension of EDAS

Overview

n-edas extends EDAS 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 decision matrix construction.

   $$\mathbf{D}=(⟨T_{ij},I_{ij},F_{ij}⟩{)}_{m\times n};s(\alpha )=\frac{1+T-2I-F}{2}$$

   Stanujkić et al. 2021 Axioms, Sec.3 Step1

2. 2

   SVN average solution: component-wise arithmetic mean.

   $${\overline{\alpha }}_j=⟨\frac{1}{m}\sum _i{T}_{ij},\frac{1}{m}\sum _i{I}_{ij},\frac{1}{m}\sum _i{F}_{ij}⟩$$

   Stanujkić et al. 2021 Axioms, Sec.3 Step2

3. 3

   PDA and NDA: signed neutrosophic distances from average.

   $$d(\alpha ,{\overline{\alpha }}_j)=\sqrt{\frac{(T-{\bar{T}}_j{)}^2+(I-{\bar{I}}_j{)}^2+(F-{\bar{F}}_j{)}^2}{3}};d_j^{\max }=\underset{k}{\max }d({\tilde{a}}_{kj},{\overline{\alpha }}_j);{\mathrm{PDA}}_{ij}=\max (0,d_{ij}\cdot 1[s({\tilde{a}}_{ij})>s({\overline{\alpha }}_j)])/d_j^{\max };{\mathrm{NDA}}_{ij}=\max (0,d_{ij}\cdot 1[s({\tilde{a}}_{ij})<s({\overline{\alpha }}_j)])/d_j^{\max }$$

   Stanujkić et al. 2021 Axioms, Sec.3 Step3

4. 4

   Weighted sums SP_i and SN_i; reverse for cost criteria.

   $$S{P}_i=\sum _j{w}_j{\mathrm{PDA}}_{ij};S{N}_i=\sum _j{w}_j{\mathrm{NDA}}_{ij}$$

   Stanujkić et al. 2021 Axioms, Sec.3 Step4

5. 5

   Normalise SP and SN.

   $$NS{P}_i=\frac{S{P}_i}{{\max }_{k}S{P}_k};NS{N}_i=1-\frac{S{N}_i}{{\max }_{k}S{N}_k}$$

   Stanujkić et al. 2021 Axioms, Sec.3 Step5

6. 6

   Appraisal score; rank descending.

   $$A{S}_i=\frac{1}{2}(NS{P}_i+NS{N}_i);A{S}_i\in [0,1];\text{rank descending}$$

   Stanujkić et al. 2021 Axioms, Sec.3 Step6-7

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