UTilités Additives DIScriminantes (Additive Utility Sorting)

UTADIS sorts alternatives into Q ordered classes (best-to-worst) by learning piecewise-linear marginal utilities u_i and Q−1 class thresholds u_k from a labelled reference set with known class assignments. The LP (Eqs.(21)-(27)) minimises the total classification error F = Σ_{a∈C_1} σ⁺(a) + … + Σ_{a∈C_Q} σ⁻(a). σ⁺(a) is the LOWER-BOUND violation slack (alternative's U(a) is below the lower threshold of its class); σ⁻(a) is the UPPER-BOUND violation slack (alternative's U(a) is above the upper threshold of its class). Reference set must be labelled (DM's prior classification given). Output: U(a