MABAC - Multi-Attributive Border Approximation area Comparison

Overview

S_i can be any real number. S_i > 0 means the alternative lies above the Border Approximation Area (BAA) - it is a good alternative for that criterion. S_i < 0 means below BAA - poor performance. Alternatives above BAA across all criteria are clearly best.

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

   Linear max-min normalisation per criterion type.

   $$n_{ij}=\{\begin{array}{ll}\frac{x_{ij}-\min x_{ij}}{\max x_{ij}-\min x_{ij}}& j\in J^{+}\\ \frac{\max x_{ij}-x_{ij}}{\max x_{ij}-\min x_{ij}}& j\in J^{-}\end{array}$$

   Pamucar-Cirovic 2015, p.3018 Eq.(2)

2. 2

   Weighted normalised matrix v_ij = w_j · (n_ij + 1).

   $$v_{ij}=w_j(n_{ij}+1)$$

   Pamucar-Cirovic 2015, p.3018 Eq.(3)

3. 3

   Border Approximation Area (BAA) per criterion: geometric mean.

   $$g_j=(\prod _{i=1}^m{v}_{ij}{)}^{1/m}$$

   Pamucar-Cirovic 2015, p.3019 Eq.(4)

4. 4

   Distance from BAA: q_ij = v_ij − g_j.

   $$q_{ij}=v_{ij}-g_j$$

   Pamucar-Cirovic 2015, p.3019 Eq.(5)

5. 5

   Alternative score S_i = Σ q_ij and descending ranking.

   $$S_i=\sum _{j=1}^n{q}_{ij}$$

   Pamucar-Cirovic 2015, p.3019 Eq.(6)

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

• Constant criterion column (max = min): normalisation denominator is zero - check E-4.

• BAA uses geometric mean, so all v_ij must be positive - the +1 shift in F2 ensures this when normalised values are in [0,1].

Works with

How to cite