N-SPOTIS - Neutrosophic extension of SPOTIS

Overview

n-spotis extends SPOTIS 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 scores; pre-specified bounds and ideal.

   $$s_{ij}=\frac{1+T_{ij}-2I_{ij}-F_{ij}}{2}\text{clipped to }[s_j^{\min },s_j^{\max }];s_j^{\ast }=s_j^{\max }(j\in {\Omega }_b),s_j^{\min }(j\in {\Omega }_c)$$

   Dezert et al. 2020, Sec.3 Step1-2

2. 2

   Normalised distance from ideal within fixed bounds.

   $$p_{ij}=\frac{|s_{ij}-s_j^{\ast }|}{s_j^{\max }-s_j^{\min }},p_{ij}\in [0,1]$$

   Dezert et al. 2020, Sec.3 Step3

3. 3

   SPOTIS score D_i; rank ascending (lower = better).

   $$D_i=\sum _{j=1}^n{w}_j{p}_{ij};\text{rank ascending}$$

   Dezert et al. 2020, Sec.3 Step4-5

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