Full Consistency Method (FUCOM)
FUCOM is a subjective weighting method that provides consistent criterion weights with only \(n-1\) comparisons. It reduces the error margin often found in AHP or BWM.
1. Rank Criteria:
Rank criteria by significance: \(C_{j(1)} > C_{j(2)} > … > C_{j(n)}\)
Rank criteria by significance: \(C_{j(1)} > C_{j(2)} > … > C_{j(n)}\)
2. Determine Comparative Priority (\(\phi\)):
Define \(\phi_{k/(k+1)}\) as the advantage of \(C_{j(k)}\) over \(C_{j(k+1)}\).
Define \(\phi_{k/(k+1)}\) as the advantage of \(C_{j(k)}\) over \(C_{j(k+1)}\).
3. Mathematical Conditions:
Condition 1: \(\frac{w_k}{w_{k+1}} = \phi_{k/(k+1)}\)
Condition 2: \(\frac{w_k}{w_{k+2}} = \phi_{k/(k+1)} \times \phi_{(k+1)/(k+2)}\)
Condition 1: \(\frac{w_k}{w_{k+1}} = \phi_{k/(k+1)}\)
Condition 2: \(\frac{w_k}{w_{k+2}} = \phi_{k/(k+1)} \times \phi_{(k+1)/(k+2)}\)
Solved Example: Software Choice
Goal: Weight 4 criteria: Functionality, Price, Security, Support.
Step 1: Rank Criteria
1. Security (C3) > 2. Functionality (C1) > 3. Price (C2) > 4. Support (C4)
1. Security (C3) > 2. Functionality (C1) > 3. Price (C2) > 4. Support (C4)
Step 2: Define Comparative Priorities (\(\phi\))
– \(\phi_{Sec/Func} = 1.2\) (Security is 20% more important than Functionality)
– \(\phi_{Func/Price} = 1.5\)
– \(\phi_{Price/Supp} = 1.3\)
– \(\phi_{Sec/Func} = 1.2\) (Security is 20% more important than Functionality)
– \(\phi_{Func/Price} = 1.5\)
– \(\phi_{Price/Supp} = 1.3\)
Step 3: Calculating Weights
Let \(w_{Supp} = 1\).
\(w_{Price} = 1 \times 1.3 = 1.3\)
\(w_{Func} = 1.3 \times 1.5 = 1.95\)
\(w_{Sec} = 1.95 \times 1.2 = 2.34\)
Sum: 1 + 1.3 + 1.95 + 2.34 = 6.59.
Normalized weights: Sec: 0.355, Func: 0.296, Price: 0.197, Supp: 0.152.
Let \(w_{Supp} = 1\).
\(w_{Price} = 1 \times 1.3 = 1.3\)
\(w_{Func} = 1.3 \times 1.5 = 1.95\)
\(w_{Sec} = 1.95 \times 1.2 = 2.34\)
Sum: 1 + 1.3 + 1.95 + 2.34 = 6.59.
Normalized weights: Sec: 0.355, Func: 0.296, Price: 0.197, Supp: 0.152.
Step 4: Alternative Ranking
| Alt | Weights applied | Score |
|---|---|---|
| Software A | (0.35×0.8)+(0.29×0.7)… | 0.742 |
| Software B | (0.35×0.6)+(0.29×0.9)… | 0.685 |
Interactive FUCOM Calculator
Rank: 1 = Most Important, 4 = Least Important
| Criteria | Rank (1-4) | \(\phi\) (vs next rank) |
|---|---|---|
| Attr 1 | ||
| Attr 2 | ||
| Attr 3 | ||
| Attr 4 | – |
Alternative Evaluation
| Alt | Attr 1 | Attr 2 | Attr 3 | Attr 4 |
|---|---|---|---|---|
| A1 | ||||
| A2 | ||||
| A3 | ||||
| A4 |
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