Grey-MABAC - Grey extension of MABAC

Overview

grey-mabac extends MABAC to handle Grey uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Grey Interval Number (GIN: [x̲, x̄]) algebra. The final scores are defuzzified via whitenisation: (x̲ + x̄)/2 before ranking.

Output

utility, higher is better

Data

Grey Number, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Grey MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

How it works

1. 1

   Normalize grey matrix; whiten v̂_ij=½(v_ij^L+v_ij^U); weight: t̃_ij=w_j·v̂_ij.

   $$\begin{gathered} {\hat{v}}_{ij}=\frac{1}{2}(v_{ij}^L+v_{ij}^U); \\ {\tilde{t}}_{ij}=w_j{\hat{v}}_{ij} \end{gathered}$$

   Pamucar-Cirovic 2015; Deng 1989

2. 2

   Grey BAA: ḡ_j = (Π_i t̃_ij)^(1/m).

   $${\bar{g}}_j=(\prod _{i=1}^m{\tilde{t}}_{ij}{)}^{1/m}$$

   Pamucar-Cirovic 2015 §BAA

3. 3

   Signed distance: q_ij = t̃_ij - ḡ_j. Sum S_i = Σ_j q_ij. Rank descending.

   $$\begin{gathered} q_{ij}={\tilde{t}}_{ij}-{\bar{g}}_j; \\ {S}_i=\sum _j{q}_{ij}; \\ \text{rank descending} \end{gathered}$$

   Pamucar-Cirovic 2015 §signed distance

Fits when / Look elsewhere when

Assumptions to verify

• Decision matrix entries are valid Grey 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 GIN: x̲ ≤ x̄ (lower and upper bounds of interval) before computation.

• Defuzzification method affects ranking: whitenisation: (x̲ + x̄)/2 is the canonical choice but alternatives exist.

Works with

How to cite