MAUT Aggregation models (n = 3)
| Model | Formula |
|---|---|
| Additive with linear value function | u(x) = w1x1 + w2x2 + w3x3 |
| Additive | u(x) = w1u1(x)1 + w2u2(x2) + w3u2(x3) |
| Multiplicative (extended) | u(x) = w1u1(x1) + w2u2(x2) + w3u2(x3) + ww1w2u1(x1)u2(x2) + ww1w3u1(x1)u3(x3) + ww2w3u2(x2)u3(x3) + w2w1w2w3u1(x)1u2(x2)u3(x3) |
| Multiplicative (compact) | 1 + wu(x) = [1 + ww1u1(x1)][1 + ww2u2(x2)] [1 + ww3u3(x3)] |
| Multi-linear | u(x) = w1u1(x1) + w2u2(x2) + ww3u3(x3) + w1,2u1(x1)u2(x2) + w1,3u1(x1)u3(x3) + w2,3u2(x2)u3(x3) + w1,2,3u1(x1)u2(x2)u3(x3) |
| Model | Formula |
|---|---|
| Additive with linear value function | u(x) = w1x1 + w2x2 + w3x3 |
| Additive | u(x) = w1u1(x)1 + w2u2(x2) + w3u2(x3) |
| Multiplicative (extended) | u(x) = w1u1(x1) + w2u2(x2) + w3u2(x3) |
| Multiplicative (compact) | 1 + wu(x) = [1 + ww1u1(x1)][1 + ww2u2(x2)] |
| Multi-linear | u(x) = w1u1(x1) + w2u2(x2) + ww3u3(x3) |
Notes:
u: Overall value function; x: Evaluation object; xi: Measurement (level, degree) of x on attribute i; ui: Single-attribute value function; wi: Weight of attribute i