REGIME - Ordinal multi-criteria method based on pairwise regime analysis

Overview

S_i can be any real number. Higher S means greater net pairwise dominance. S_i = 0 means balanced wins and losses. REGIME is sign-based (only direction of difference matters, not magnitude) - it is robust to outliers and scale differences. It is similar to APLOCO but without normalisation.

Output

net agreement, 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

   For each ordered pair (A_i, A_k), compute regime vector e_ik: e_ik,j = +1 if A_i dominates A_k on criterion j (adjusted for direction), −1 if dominated, 0 if equal.

   $$e_{ik,j}=\text{sign}((x_{ij}-x_{kj})\cdot d_j),d_j=+1\text{ (benefit)},-1\text{ (cost)}$$

   Hinloopen et al. 1983, p.84

2. 2

   Compute weighted regime score R_ik = Σ_j w_j · e_ik,j. Net dominance score for A_i: S_i = Σ_k R_ik. Rank descending.

   $$R_{ik}=\sum _{j=1}^n{w}_j{e}_{ik,j};S_i=\sum _{k\ne i}{R}_{ik}$$

   Hinloopen et al. 1983, p.85

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

• •if A_i dominates A_k on criterion j (adjusted for direction), −1 if dominated, 0 if equal.

• All alternatives identical on a criterion: e_ik,j = 0 for all pairs - the criterion contributes 0 to all scores.

Works with

How to cite