MEREC - MEthod based on the Removal Effects of Criteria

Overview

MEREC assigns higher weight to criteria whose removal causes greater change in the overall performance ranking. It is fully data-driven and particularly sensitive to criteria that provide unique discriminating power. Criteria with highly similar performance across alternatives get lower weight.

Output

Weight, higher is better

Data

Crisp, complete numeric matrix

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

Any (objective weighting)

How it works

1. 1

   Logarithmic normalisation x'_ij ∈ [0,1].

   $$x_{ij}^{\prime }=\{\begin{array}{ll}\frac{{\min }_k{x}_{kj}}{x_{ij}}& j\in J^{+}\\ \frac{x_{ij}}{{\max }_k{x}_{kj}}& j\in J^{-}\end{array}$$

   Keshavarz-Ghorabaee 2021, p.6 Eq.(2)

2. 2

   Overall performance S_i with all criteria.

   $$S_i=\ln (1+(\frac{1}{n}\sum _{j=1}^n|\ln (x_{ij}^{\prime })|\left)\right)$$

   Keshavarz-Ghorabaee 2021, p.6 Eq.(3)

3. 3

   Performance S'_ij when criterion j is removed.

   $$S_{ij}^{\prime }=\ln (1+(\frac{1}{n}\sum _{k\ne j}|\ln (x_{ik}^{\prime })|\left)\right)$$

   Keshavarz-Ghorabaee 2021, p.6 Eq.(4)

4. 4

   Removal effect E_j = Σ |S_i − S'_ij|.

   $$E_j=\sum _{i=1}^m|S_i-S_{ij}^{\prime }|$$

   Keshavarz-Ghorabaee 2021, p.6 Eq.(5)

5. 5

   MEREC weights w_j = E_j / Σ E_k.

   $$w_j=\frac{E_j}{{\sum }_{k=1}^n{E}_k}$$

   Keshavarz-Ghorabaee 2021, p.7 Eq.(6)

Look elsewhere when

Assumptions to verify

• Decision matrix exists with measurable criteria
• Sufficient inter-alternative variation per criterion

Edge cases and pitfalls

• •when criterion j is removed.

• All alternatives identical on all criteria: E_j = 0 for all j, weights undefined - check data.

• n=1: S'_ij undefined (removing the only criterion leaves nothing). MEREC requires n ≥ 2.

• Sensitive to individual cell perturbations: small data changes can shift S_i and S'_ij non-trivially due to log compression. Run S.data_perturbation.

• Direction matters: benefit uses min/x, cost uses x/max. Wrong direction inverts removal-effect meaning for that criterion.

Works with

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