Dichotomous Attribute

See: Binary Attribute, Dichotomous Preferences.

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References

2017a

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Dichotomy Retrieved:2017-6-18.
  • A dichotomy is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be
    • jointly exhaustive: everything must belong to one part or the other, and
    • mutually exclusive: nothing can belong simultaneously to both parts.
  • Such a partition is also frequently called a bipartition.

    The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other.

    Treating continuous variables or multicategorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling purposes.

2017b

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Dichotomous_preferences Retrieved:2017-6-18.
  • In economics, dichotomous preferences (DP) are preference relations that divide the set of alternatives to two subsets: "Good" versus "Bad".

    From ordinal utility perspective, DP means that for every two alternatives [math]\displaystyle{ X,Y }[/math] : : [math]\displaystyle{ X \preceq Y \iff X \in Bad \text{ or } Y \in Good }[/math] : [math]\displaystyle{ X \prec Y \iff X \in Bad \text{ and } Y \in Good }[/math] From cardinal utility perspective, DP means that for each agent, there are two utility levels: low and high, and for every alternative [math]\displaystyle{ X }[/math] : : [math]\displaystyle{ u(X) = u_{low} \iff X\in Bad }[/math] : [math]\displaystyle{ u(X) = u_{high} \iff X\in Good }[/math]

2000

• (Witten & Frank, 2000) ⇒ Ian H. Witten, and Eibe Frank. (2000). “Data Mining: Practical Machine Learning Tools and Techniques with Java implementations." Morgan Kaufmann.

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