Mathematics and statistics

Fuzzy control system

A fuzzy control system is a control system whose controller uses fuzzy logic and linguistic rules, converting a human operator's heuristic knowledge into automatic control strategy.

The Fuzzy Delphi method is a consensus-building and forecasting technique that combines the classical Delphi expert survey with fuzzy set theory, letting experts answer with fuzzy numbers; it was first proposed in 1985.

Fuzzy goal programming

Fuzzy goal programming (FGP) is a multi-objective optimization method that treats imprecise targets as fuzzy sets with membership functions, introduced by Ram Narasimhan in 1980.

Fuzzy logic

Fuzzy logic, also called mathematical fuzzy logic, is a form of reasoning that assigns propositions degrees of truth between 0 and 1, introduced by Lotfi A. Zadeh in 1965.

Fuzzy number

A fuzzy number is a fuzzy set on the real line representing an imprecise quantity such as "about 5", formulated by Didier Dubois and Henri Prade in 1978.

Fuzzy programming

Fuzzy programming is a family of optimization methods in operations research that models imprecise objectives and constraints as fuzzy sets, then converts them into solvable crisp programs.

Fuzzy regression

Fuzzy regression is a statistical modeling method that uses fuzzy numbers as coefficients and predictions, intended for small or vague samples where ordinary regression is problematic.

Fuzzy set

A fuzzy set is a class in which membership is a matter of degree from 0 to 1, a concept introduced by Lotfi Zadeh in his 1965 paper "Fuzzy sets."

Fuzzy sphere

The fuzzy sphere is a noncommutative geometry that replaces functions on the two-sphere with finite matrix algebras, introduced by John Madore in 1992 as a symmetry-preserving cutoff.

Fuzzy TOPSIS

Fuzzy TOPSIS is a multi-criteria decision-making method that ranks alternatives when ratings and weights are vague, combining TOPSIS with fuzzy set theory, introduced by Chen-Tung Chen in 2000.

G-computation

G-computation, also called the parametric g-formula, is a statistical method for estimating the causal effect of a treatment from observational data, introduced by James Robins in 1986.

Gabor wavelet

A Gabor wavelet is a sinusoidal carrier multiplied by a Gaussian envelope, used for localized time-frequency analysis of signals and for feature extraction from images.

Galois cohomology

Galois cohomology is the cohomology theory of Galois groups, the right derived functors of the invariants functor, central to class field theory, the Brauer group, and Wiles's proof of Fermat's last theorem.

Galois connection

A Galois connection, also known as a Galois correspondence, is a pair of monotone maps between partially ordered sets where f(p) ≤ q holds exactly when p ≤ g(q), named for Évariste Galois.

Galois cover

A Galois cover is a cover of curves or schemes whose function field extension is a Galois extension, equivalently one with a transitive group of deck transformations.

Galois extension

A Galois extension is an algebraic field extension that is both normal and separable, equivalently the splitting field of a separable polynomial over the base field.

Galois group

A Galois group is the group of automorphisms of a field extension fixing the base field, introduced by Évariste Galois to study when equations are solvable by radicals.

Galois module

A Galois module, also known as a Galois representation, is an abelian group with a compatible action of a Galois group; the term also names the theory of rings of integers.

Galois representation

A Galois representation is a continuous homomorphism from the absolute Galois group of a field to invertible matrices, central to Wiles's proof of Fermat's last theorem.

Galois theory

Galois theory is the branch of algebra, created by Évariste Galois, that associates to each field extension a Galois group and proves that general polynomial equations of degree 5 and higher cannot be solved by radicals.

Galton–Watson process

The Galton–Watson process, or Bienaymé–Galton–Watson process, is a branching process in which each individual independently produces offspring from one fixed distribution, posed by Galton in 1873.

Gambler's fallacy

The gambler's fallacy, also called the Monte Carlo fallacy, is the mistaken belief that an outcome absent from a random sequence becomes more likely on the next trial.

Gambler's ruin

Gambler's ruin is a classical probability problem in which a gambler makes repeated unit bets, and the question is whether the fortune reaches a target before zero.

Game semantics

Game semantics is a style of denotational semantics interpreting types as games and programs as strategies, arising in the early 1990s from the full abstraction problem for PCF.

Game theory

Game theory is the mathematical study of strategic interaction, a family of models founded on von Neumann's 1928 minimax theorem and Nash's 1950 equilibrium, now central to economics.

Gamma distribution

The gamma distribution is a continuous probability distribution for positive random variables defined by shape and scale parameters; it is used as a lifetime model and Bayesian prior.

Gamma function

The gamma function, or Γ function, is a mathematical function extending the factorial to complex numbers, so Γ(z) = (z − 1)! for positive integers; Euler introduced it in 1729.

Gamma matrices

The gamma matrices, or Dirac matrices, are square matrices satisfying the Clifford anticommutation relation {γ, γ} = 2η, appearing as coefficients of the Dirac equation in relativistic quantum mechanics.

Gamma process

The gamma process, or gamma subordinator, is a Lévy process with independent, nonnegative gamma-distributed increments, applied in reliability and as the time change behind the Variance Gamma option-pricing model.