ROC - Rank Order Centroid weights (rank-based surrogate weights)

Overview

ROC weights are surrogate weights derived purely from the rank order - no numeric importance judgements needed. They are the expected value of the weights given only their ordering. w_1>w_2>…>w_n always holds. Most weight is concentrated at rank 1.

Output

Weight, higher is better

Data

Crisp, expert input required

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

Expert-driven decision making, MAGDM

How it works

1. 1

   ROC weight for the criterion with rank r (out of n): w_r = (1/n) Σ_{k=r}^{n} (1/k). This is the centroid of the simplex constrained by the rank ordering.

   $$w_r=\frac{1}{n}\sum _{k=r}^n\frac{1}{k},r=1,\dots ,n$$

   Barron & Barrett 1996, p.1517 Eq.(2) (pending PDF page verification)

Fits when / Look elsewhere when

Assumptions to verify

• Domain experts available
• Experts can express consistent comparisons

Edge cases and pitfalls

• ROC assigns weight only from rank, not magnitude - if the DM knows ratio importance (e.g. C1 is twice as important as C2), use direct rating (SMART) or BWM instead.

Works with

How to cite