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 theo ...
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, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered set ...
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 elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over Set (mathematics), sets and is a new set of ordered pairs consisting of ele ...
. One specific variation of weak ordering, a
total preorder
In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered set ...
(= 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 in machine learning, which is a classification method based on observed preference information. In the view of supervised learning, preference learning trains on a set of items which have preferences toward labels o ...
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 other social sciences, preference is the order that an agent gives to alternatives based on their relative utility. A process which results in an "optimal choice" (whether real or theoretical). Preferences are evaluations and conc ...
.
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