EDAS - Evaluation Based on Distance from Average Solution

Overview

AS_i ∈ [0,1]. Higher AS means the alternative is more above the average solution (positively) and less below it (negatively). EDAS is robust when the ideal and anti-ideal cannot be identified reliably, since it uses the average as reference instead.

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

   Compute the Average Solution (AV) per criterion: AV_j = (1/m) Σ_i x_ij.

   $$A{V}_j=\frac{1}{m}\sum _{i=1}^m{x}_{ij}$$

   Keshavarz-Ghorabaee 2015, p.439 Eq.(3)

2. 2

   Positive Distance from Average (PDA): direction-aware deviation above AV.

   $$PD{A}_{ij}=\{\begin{array}{ll}\frac{\max (0,x_{ij}-A{V}_j)}{A{V}_j}& j\in J^{+}\\ \frac{\max (0,A{V}_j-x_{ij})}{A{V}_j}& j\in J^{-}\end{array}$$

   Keshavarz-Ghorabaee 2015, p.439 Eq.(4)

3. 3

   Negative Distance from Average (NDA): direction-aware deviation below AV.

   $$ND{A}_{ij}=\{\begin{array}{ll}\frac{\max (0,A{V}_j-x_{ij})}{A{V}_j}& j\in J^{+}\\ \frac{\max (0,x_{ij}-A{V}_j)}{A{V}_j}& j\in J^{-}\end{array}$$

   Keshavarz-Ghorabaee 2015, p.439 Eq.(5)

4. 4

   Weighted sums SP_i and SN_i across criteria.

   $$S{P}_i=\sum _{j=1}^n{w}_{j}PD{A}_{ij},S{N}_i=\sum _{j=1}^n{w}_{j}ND{A}_{ij}$$

   Keshavarz-Ghorabaee 2015, p.439 Eqs.(6)-(7)

5. 5

   Normalize SP, SN by their maxima.

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

   Keshavarz-Ghorabaee 2015, p.440 Eqs.(8)-(9)

6. 6

   Appraisal Score AS_i and descending ranking.

   $$A{S}_i=\frac{1}{2}(NS{P}_i+NS{N}_i),0\le A{S}_i\le 1$$

   Keshavarz-Ghorabaee 2015, p.440 Eq.(10)

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

• All alternatives on one side of the average: if all x_ij ≥ AV_j for all i, then NDA_ij = 0 ∀i,j and NSN_i = 0 (or undefined) - handle degenerate case.

• AV_j = 0 for any criterion: division-by-zero in PDA/NDA - check E-4.

Works with

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