EVAMIX - EVAluation of MIXed data

Overview

S_i can be any real number. Higher S means greater net dominance over other alternatives across both ordinal and cardinal criteria. EVAMIX is designed for mixed-scale problems where some criteria are measured on cardinal scales (ratio, interval) and others only on ordinal scales (rankings, categories).

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

   For each ordered pair (A_i, A_k): compute ordinal dominance score OD_ik = Σ_{j∈ordinal} w_j · sign(x_ij − x_kj)·d_j and cardinal dominance score CD_ik = Σ_{j∈cardinal} w_j · (n_ij − n_kj) where n_ij is min-max normalised.

   $$O{D}_{ik}=\sum _{j\in \text{ordinal}}{w}_j\cdot \text{sign}((x_{ij}-x_{kj})\cdot d_j);C{D}_{ik}=\sum _{j\in \text{cardinal}}{w}_j\cdot (n_{ij}-n_{kj})$$

   Voogd 1983, p.222-225

2. 2

   Compute overall dominance score D_ik = w_ord · OD_ik + w_card · CD_ik where w_ord = Σ_{j∈ordinal} w_j, w_card = Σ_{j∈cardinal} w_j. Net score S_i = Σ_k D_ik. Rank descending.

   $$D_{ik}=w_{\text{ord}}\cdot O{D}_{ik}+w_{\text{card}}\cdot C{D}_{ik};S_i=\sum _{k\ne i}{D}_{ik}$$

   Voogd 1983, p.225

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

• All criteria cardinal: EVAMIX reduces to a standard pairwise dominance method. All ordinal: reduces to sign-based (REGIME-like).

Works with

How to cite