RAPS - Ranking of Alternatives based on Preference Strength

Overview

R_i ∈ [0,1]. R_i = 0.5 means equal preference wins and losses. Higher R means stronger relative preference advantage. RAPS is designed to be rank-reversal free: it normalises preference strength by the total (PS_ik + PS_ki), making each pairwise comparison self-contained.

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

   Min-max normalise to [0,1].

   $$r_{ij}=\frac{x_{ij}-x_j^{\min }}{x_j^{\max }-x_j^{\min }}\text{ (benefit)};r_{ij}=\frac{x_j^{\max }-x_{ij}}{x_j^{\max }-x_j^{\min }}\text{ (cost)}$$

   Dezert & Tchamova 2021, p.15

2. 2

   For each pair (A_i, A_k), compute pairwise preference strength PS_ik = Σ_j w_j · max(0, r_ij − r_kj).

   $$P{S}_{ik}=\sum _{j=1}^n{w}_j\max (0,r_{ij}-r_{kj})$$

   Dezert & Tchamova 2021, p.15 Eq.(6)

3. 3

   Compute RAPS score R_i = Σ_{k≠i} PS_ik / Σ_{k≠i}(PS_ik + PS_ki). Rank descending.

   $$R_i=\frac{{\sum }_{k\ne i}P{S}_{ik}}{{\sum }_{k\ne i}(P{S}_{ik}+P{S}_{ki})}$$

   Dezert & Tchamova 2021, p.16 Eq.(7)

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

• PS_ik + PS_ki = 0: two alternatives tied on all criteria - handle as R = 0.5 (neutral).

Works with

How to cite