Live briefing
Everything about Preorder
Reflexive and transitive binary relation
In mathematics, in particular in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest that preorders are almost partial orders, but not quite, as they are not necessarily antisymmetric. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: PreorderA 5-minute orientation
- Skim a recent paper: Consensus modeling with interactive utility and partial preorder of decision-makers, involving fairness and tolerant behaviorInfluential work since 2022
- Pick up a classic book: Code Name BananasThe most-reprinted book on the subject
- Read the landmark paper: Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP methodCited 212 times
- Go sideways: Weak orderingA closely related topic
- Go sideways: Homogeneous relationA closely related topic
📖 Definitions
Verb To order (goods or services) in advance, before they are available.
Verb To sort or arrange beforehand.
Noun An order for goods or services placed in advance.
Noun A binary relation that is reflexive and transitive.
🏆 Landmark papers (most cited)
Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method
Advance Demand Information, Price Discrimination, and Preorder Strategies
Fuzzy preorder and fuzzy topology
“Preorder-online, pickup-in-store” strategy for a dual-channel retailer
An efficiency preorder for processes
Optimal Preorder Strategy with Endogenous Information Control
Advance Selling to Strategic Consumers: Preorder Contingent Production Strategy with Advance Selling Target
A Distance-Based Collective Preorder Integrating the Relative Importance of the Group's Members
🆕 Influential since 2022
Consensus modeling with interactive utility and partial preorder of decision-makers, involving fairness and tolerant behavior
An automatic distillation sequence synthesis framework based on a preorder traversal algorithm
A note on the admissibility of the centroid-based preorder for fuzzy numbers
Order embedding theorems and multi-utility representation of the preorder
A companion preorder to G-majorization and a Tarski type fixed-point theorem section: convex analysis
📚 Books worth reading
Code Name BananasDavid Walliams · 2020
No BrainerJeff Kinney · 2023
One Impossible LabyrinthMatthew Reilly · 2022
Life of crimeKimberley Chambers · 2018- 📕InterpreterBrooke Robinson · 2023
NightshadeMichael Connelly · 2025- 📕CutRichard Armitage · 2025
The Night Is DefyingChloe C. Peñaranda · 2025
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Weak ordering In 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…
- Homogeneous relation In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian…
- Equivalence relation In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments…
- Glossary of order theory Look up Appendix:Glossary of order theory in Wiktionary, the free dictionary. This is a glossary of some terms used in various branches of mathematics…
- Transitive relation In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates…
- Partially ordered set In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The…
- Binary relation In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set (possibly the same) called the…
- Relation (mathematics) In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. As an example, "is less than" is…