RAT - Reference Alternative based Aggregation Technique

Overview

Apply F.steps in order; final score determines descending ranking.

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

   Build ranking matrix A = [r_ij]_{m×n} where rows are alternatives and columns are rankings from n different MCDM techniques.

   $$A=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1n}\\ r_{21}& r_{22}& \cdots & r_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ r_{m1}& r_{m2}& \cdots & r_{mn}\end{array}\right]$$

   Orakçı 2024, p.41 Eq.(22)

2. 2

   Select the first alternative as reference (A_1); its aggregated value is defined as zero.

   $$A_1=0\text{(referans alternatif)}$$

   Orakçı 2024, p.41 Sec.2.1 Step 2

3. 3

   Compute aggregated value A_k for k = 1..m via the signum-weighted Euclidean-square-difference sum: positive sign if reference ranks better than alternative k in column j.

   $$A_k=\sum _{i=1}^n\sum _{j=1}^n\mathrm{sgn}(r_{1j}-r_{kj})\cdot \sqrt{|r_{1j}^2-r_{kj}^2|},k=1,2,\dots ,m$$

   Orakçı 2024, p.41 Eq.(23)

4. 4

   Sort A_k values in descending order; the alternative with the highest A_k receives rank 1.

   $$\text{Rank}(A_i)\propto -A_i,i=1,\dots ,m$$

   Orakçı 2024, p.42 Step 4

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

• •zero.
• •if reference ranks better than alternative k in column j.

• Applying RAT without verifying this assumption.

  Requirement: Criteria preferences are independent (no synergistic interactions)

• Applying RAT without verifying this assumption.

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

• Applying RAT without verifying this assumption.

  Requirement: Decision matrix is complete (no missing values)

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

  An alternative method is recommended in this situation.

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

  An alternative method is recommended in this situation.

Works with

How to cite