CIMAS - Criterion Impact MeAsurement System

Overview

L_j ∈ [0,1], Σ L_j = 1. Higher L_j means criterion j is more important. CIMAS amplifies criteria where experts disagree most strongly (large weighted range), reflecting that disagreement carries information about importance.

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

Supplier selection, expert-driven group weighting

How it works

1. 1

   Uzman ağırlıklarını deneyim yıllarından hesapla.

   $$W^{E_i}=E_i/{\Sigma }_i{E}_i$$

   Bošković et al. 2025, p.338 Eq.(1)

2. 2

   Giriş veri matrisini sütun-bazlı (uzmanlar üzerinden) lineer-toplam normalize et.

   $$x{\ast }_{i}j=x_{i}j/{\Sigma }_i{x}_{i}j$$

   Bošković et al. 2025, p.339 Eq.(2)

3. 3

   Normalleştirilmiş matrisin her satırını uzman ağırlığıyla çarp.

   $$\hat{x}{\ast }_{i}j=x{\ast }_{i}j\cdot W^{E_i}$$

   Bošković et al. 2025, p.339 Eq.(3)

4. 4

   Her kriter sütununda maksimum ve minimum bul.

   R_j_max = max_i x̂*_ij; R_j_min = min_i x̂*_ij

   Bošković et al. 2025, p.340 Eqs.(4)-(5)

5. 5

   Her kriter için max−min farkı.

   B_j = R_j_max − R_j_min

   Bošković et al. 2025, p.340 Eq.(6)

6. 6

   Final kriter ağırlıkları.

   $$L_j=B_j/{\Sigma }_j{B}_j$$

   Bošković et al. 2025, p.340 Eq.(7)

Fits when / Look elsewhere when

Assumptions to verify

• Domain experts available
• Experts can express consistent comparisons

Edge cases and pitfalls

• All experts give identical ratings on criterion j → B_j = 0 and L_j = 0. This is methodologically correct: zero variance among experts means zero information signal. Handle by either dropping the criterion or noting it explicitly.

• CIMAS amplifies expert disagreement - if experts are biased rather than knowledgeable, the method propagates bias. Validate with Reliability Index RI (Eq.8); RI < 0.1 indicates results acceptable.

Works with

How to cite