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Table 1 Overview of a number of standard combination functions

From: Modelling and analysis of the dynamics of adaptive temporal–causal network models for evolving social interactions

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 ) with λ > 0

sisum(..)

Scaled sum with interaction terms

(V 1 + + V k ) + 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