The term preference relation is used to refer to orderings that describe human
preference
In psychology, economics and philosophy, preference is a technical term usually used in relation to choosing between alternatives. For example, someone prefers A over B if they would rather choose A than B. Preferences are central to decision the ...
s for one thing over an other.
* In mathematics, preferences may be modeled as a
weak ordering
In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set (mathematics), set, some of whose members may be Tie (draw), tied with each other. Weak orders are a general ...
or a
semiorder
In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are compared by their scores and where scores within a given margin of error are deemed incompar ...
, two different types of
binary relation
In mathematics, a binary relation associates some elements of one Set (mathematics), set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs ...
. One specific variation of weak ordering, a
total preorder (= a connected, reflexive and transitive relation), is also sometimes called a preference relation.
* In computer science, machine learning algorithms are used to infer preferences, and the binary representation of the output of a
preference learning
Preference learning is a subfield of machine learning that focuses on modeling and predicting preferences based on observed preference information. Preference learning typically involves supervised learning using datasets of pairwise preference com ...
algorithm is called a preference relation, regardless of whether it fits the weak ordering or semiorder mathematical models.
* Preference relations are also widely used in economics; see
preference (economics)
In economics, and in other social sciences, preference refers to an order by which an Agent (economics), agent, while in search of an "optimal choice", ranks alternatives based on their respective utility. ''Preferences'' are evaluations that conc ...
.
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