WEDBA - Weighted Euclidean Distance Based Approach

Overview

Apply F.steps in order.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Alternative selection, Supplier evaluation

How it works

1. 1

   Decision matrix X = [x_ij]_{m×n}.

   $$X=[x_{ij}{]}_{m\times n}$$

   Dadelo 2014, Eq.(1)

2. 2

   Vector normalisation r_ij.

   $$r_{ij}=\frac{x_{ij}}{\sqrt{{\sum }_{i=1}^m{x}_{ij}^2}}$$

   Dadelo 2014, Eq.(2)

3. 3

   Weighted matrix v_ij = w_j r_ij.

   $$v_{ij}=w_j{r}_{ij}$$

   Dadelo 2014, Eq.(3)

4. 4

   Best v_j^+ and worst v_j^- per criterion direction.

   $$v_j^{+}=\underset{i}{\max }{v}_{ij}(J^{+}),\min (J^{-});v_j^{-}\text{ aksi}$$

   Dadelo 2014, Eq.(4)

5. 5

   Weighted Euclidean D_i^+ and D_i^-.

   $$D_i^{+}=\sqrt{\sum _j(v_{ij}-v_j^{+}{)}^2},D_i^{-}=\sqrt{\sum _j(v_{ij}-v_j^{-}{)}^2}$$

   Dadelo 2014, Eq.(5)

6. 6

   Z_i = D_i^- / (D_i^+ + D_i^-); descending ranking.

   $$Z_i=\frac{D_i^{-}}{D_i^{+}+D_i^{-}},0\le Z_i\le 1$$

   Dadelo 2014, Eq.(6)

Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Edge cases and pitfalls

• Applying WEDBA without verifying this assumption.

  Requirement: Criteria preferences are independent (no synergistic interactions)

• Applying WEDBA without verifying this assumption.

  Requirement: Compensation is acceptable: high score on one criterion can offset low on another

• Applying WEDBA without verifying this assumption.

  Requirement: Decision matrix is complete (no missing values)

• Using WEDBA when: Criteria strongly correlated → consider DEMATEL/ANP for interdependence.

  An alternative method is recommended in this situation.

• Using WEDBA when: Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE).

  An alternative method is recommended in this situation.

Works with

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