Name | Description | Formula c( V 1,…, V k )= |
---|---|---|
sum(..) | Sum | \(V_1 + \cdots + V_k\) |
product(..) cproduct(..) | Product Complement product | \(V_1*\cdots *V_k\) \(1-(1-V_1)*\cdots *(1-V_k)\) k ) |
min(..) max(..) | Minimal value Maximal value | min( V 1 ,…, V k ) max( V 1 ,…, V k ) |
slogistic σ,τ (..) | Simple logistic sum | \( {1 \mathord{\left/ {\vphantom {1 {\left( {1 + {\mathbf{e}}^{{ - \sigma (V_{ 1} + \cdots + V_{k} - \tau )}} } \right)}}} \right. \kern-0pt} {\left( {1 + {\mathbf{e}}^{{ - \sigma (V_{ 1} + \cdots+ V_{k} - \tau )}} } \right)}} \) with σ, τ ≥ 0 |
alogistic σ,τ (..) | Advanced logistic sum | \( \left[ {\left( {{1 \mathord{\left/ {\vphantom {1 {\left( {1 + {\mathbf{e}}^{{ - \sigma (V_{ 1} +\cdots + V_{k} - \tau )}} } \right)}}} \right. \kern-0pt} {\left( {1 + {\mathbf{e}}^{{ - \sigma (V_{ 1} + \cdots + V_{k} - \tau )}} } \right)}}} \right) - \left( {{1 \mathord{\left/ {\vphantom {1 {\left( {1 + {\mathbf{e}}^{\sigma \tau } } \right)}}} \right. \kern-0pt} {\left( {1 + {\mathbf{e}}^{\sigma \tau } } \right)}}} \right)} \right]\left( {1 + {\mathbf{e}}^{ - \sigma \tau } } \right) \) with σ, τ ≥ 0 |
ssum λ (..) | Scaled sum | (V 1 +⋯ + V k )/λ with λ > 0 |
sisum(..) | Scaled sum with interaction terms | (V 1 +⋯ + V k )/λ + Σ ij μ ij V i V j with λ > 0 |
aproduct β (..) | Advanced product | β cproduct( V 1 ,…, V k ) + (1 − β) product( V 1 ,…, V k ) with 0 ≤ β≤1 |
aminmax β (..) | Advanced minimum and maximum | β max( V 1 ,…, V k ) + (1 − β) min( V 1 ,…, V k ) with 0 ≤ β≤1 |
aproduct-ssum β,λ (..) | Advanced product and scaled sum | aproduct β (V 0, ssum λ ( V 1 ,…, V k )) with 0 ≤ β≤1 and λ > 0 |