Revised Simos Procedure - deck-of-cards rank-based weight elicitation (Figueira & Roy 2002)

Overview

The Revised Simos procedure asks the DM to rank criteria cards from least to most important, and to insert blank cards between consecutive criteria to indicate the importance gap. More blank cards = larger gap in importance. Weights are proportional to the adjusted rank position u_j.

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

   Order criterion cards by importance; insert blank cards between equally-spaced groups; specify ratio z.

   $$\text{Cards: }{C}_{(1)},C_{(2)},\dots ,C_{(n)};\text{blank counts }{e}_k;z=w_{(n)}/w_{(1)}$$

   Figueira-Roy 2002, p.318 Sec.3

2. 2

   Non-normalised weights k_j based on positions and blank cards.

   $$k_j=1+(z-1)\cdot \frac{u_j-1}{u_n-1},u_j=\sum _{l\le j}(1+e_l)$$

   Figueira-Roy 2002, p.319 Eq.(1)

3. 3

   Normalised SIMOS weights w_j = k_j / Σ k_l.

   $$w_j=\frac{k_j}{{\sum }_{l=1}^n{k}_l}$$

   Figueira-Roy 2002, p.319 Eq.(2)

Fits when / Look elsewhere when

Assumptions to verify

• Domain experts available
• Experts can express consistent comparisons

Edge cases and pitfalls

• Blank cards add to rank gaps additively - 3 blank cards between C_j and C_{j+1} means u_{j+1} = u_j + 1 + 3 = u_j + 4, not u_j + 3.

Works with

How to cite