FUCOM - Full Consistency Method

Overview

FUCOM requires only n−1 pairwise comparisons (like SWARA) but additionally enforces transitivity via the LP, ensuring mathematical consistency. χ*=0 means perfect consistency. The LP always has a solution (unlike AHP which can be inconsistent). FUCOM is particularly efficient for large n.

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

   Rank criteria by importance C_(1) ≻ C_(2) ≻ … ≻ C_(n).

   $$C_{(1)}⪰C_{(2)}⪰\cdots ⪰C_{(n)}$$

   Pamucar 2018, p.5 Sec.3.1

2. 2

   Comparative importance vector φ_(k) of consecutive criteria.

   $${\varphi }_{(k)}=\frac{w_{(k)}}{w_{(k+1)}},k=1,\dots ,n-1$$

   Pamucar 2018, p.5 Eq.(1)

3. 3

   Min-max optimisation for weights satisfying φ + transitivity.

   $$\min \chi \text{s.t.}\left|\frac{w_{(k)}}{w_{(k+1)}}-{\varphi }_{(k)}\right|\le \chi ,\left|\frac{w_{(k)}}{w_{(k+2)}}-{\varphi }_{(k)}{\varphi }_{(k+1)}\right|\le \chi ,\sum w_j=1$$

   Pamucar 2018, p.6 Eqs.(2)-(3)

Fits when / Look elsewhere when

Assumptions to verify

• Domain experts available
• Experts can express consistent comparisons

Edge cases and pitfalls

• φ ratios < 1: all ratios must be ≥ 1 (criterion j is always ≥ as important as j+1 in ranked order).

Works with

How to cite