FUCA - Flexible and Universal Compromise Analysis

Overview

F_i ∈ [1, m] approximately. Lower F means better (lower average rank across criteria). FUCA is essentially a weighted Borda count using per-criterion ordinal ranks rather than raw values - it is robust to scale differences and outliers because only the rank order matters, not the magnitude.

Output

rank sum, lower 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

   Rank each alternative on each criterion (1 = best). For benefit: rank 1 = highest value. For cost: rank 1 = lowest value. Ties get average rank.

   $${\rho }_{ij}=\text{rank of alternative }i\text{ on criterion }j\text{ (1=best, ties=average)}$$

   Raveh 2000, p.672

2. 2

   Compute FUCA score F_i = weighted sum of per-criterion ranks. Rank ascending (lower = better).

   $$F_i=\sum _{j=1}^n{w}_j{\rho }_{ij}$$

   Raveh 2000, p.672

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

• •Ties get average rank.

• All alternatives tied on a criterion: all receive the same average rank - this criterion contributes no discrimination.

Works with

How to cite