Grey-WASPAS - Grey extension of WASPAS

Overview

grey-waspas extends WASPAS 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 (benefit/cost); whiten: v̂_ij=½(v_ij^L+v_ij^U).

   $${\hat{v}}_{ij}=\frac{1}{2}(v_{ij}^{L,\mathrm{norm}}+v_{ij}^{U,\mathrm{norm}})$$

   Zavadskas-Turskis 2012; Deng 1989

2. 2

   WSM score: Q_i^(1) = Σ_j w_j·v̂_ij.

   $$Q_i^{(1)}=\sum _j{w}_j{\hat{v}}_{ij}$$

   Zavadskas-Turskis 2012 §WSM

3. 3

   WPM score: Q_i^(2) = Π_j v̂_ij^(w_j).

   $$Q_i^{(2)}=\prod _j{\hat{v}}_{ij}^{w_j}$$

   Zavadskas-Turskis 2012 §WPM

4. 4

   Combined: Q_i = λ·Q_i^(1) + (1-λ)·Q_i^(2), λ=0.5. Rank descending.

   $$\begin{gathered} Q_i=\lambda Q_i^{(1)}+(1-\lambda )Q_i^{(2)},\lambda =0.5; \\ \text{rank descending} \end{gathered}$$

   Zavadskas-Turskis 2012 §combined WASPAS

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