Continuous-Output Set Function

A Continuous-Output Set Function is a set input-function that is a continuous-output function.

• AKA: Set Measure; [math]\displaystyle{ f:2^V \rightarrow \Re }[/math].
• Context:
  • It can range from being, based on the input size, a Unary Continuous-Output Set Function, Binary Continuous-Output Set Function, an N-ary Continuous-Output Set Function.
  • It can range from being a Strictly Positive Continuous-Output Set Function to being a Non-Positive Continuous-Output Set Function to being a Non-Negaive Continuous-Output Set Function, to being a Strictly-Negative Continuous-Output Set Function.
  • …
• Example(s):
  • a Recall Function.
  • an F1 Measure.
  • a Unary Set Function, such as the Set Cardinality Function.
  • the Event Probability Function.
  • a Set Relation, such as the Subset Relation.
  • a Transformation Function.
  • a Modular Function, Submodular Function, Supermodular Function.
  • …
• Counter-Example(s):
  • an Ordinal-Output Set Function, an Categorical-Output Set Function.
  • a Multiset Measure Function.
• See: Set, Measure Space, Normalized Set Function.

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