NMD - New Method of Determining objective criterion weights

Overview

NMD assigns higher weight to criteria whose alternatives perform further below the maximum (lower μ_j → more spread from the ideal). It is fully objective and simple to compute. Criteria where all alternatives score near 1 (all close to best) get low 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

   Apply linear-max normalisation: benefit n_ij = x_ij/max; cost n_ij = min/x_ij.

   $$n_{ij}=x_{ij}/x_j^{\max }\text{(benefit)};n_{ij}=x_j^{\min }/x_{ij}\text{(cost)}$$

   Bulut 2017, p.807 (pending PDF page verification)

2. 2

   Compute column mean μ_j of normalised matrix. Compute w_j = (1 − μ_j) / Σ_k (1 − μ_k). Higher weight for lower mean (more variation from 1 = best).

   $${\mu }_j=\frac{1}{m}\sum _i{n}_{ij};w_j=\frac{1-{\mu }_j}{{\sum }_k(1-{\mu }_k)}$$

   Bulut 2017, p.807 Eq. (pending PDF page verification)

Look elsewhere when

Assumptions to verify

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

Edge cases and pitfalls

• If μ_j = 1 for some criterion (all alternatives are the best), then (1−μ_j)=0 → w_j=0. The criterion is uninformative.

Works with

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