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T-norm

Index T-norm

In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. [1]

42 relations: Archimedean property, Associative property, Łukasiewicz logic, Binary operation, Commutative property, Construction of t-norms, Continuous function, De Morgan's laws, Degree of truth, Distributive property, Event (probability theory), Function (mathematics), Fuzzy logic, Fuzzy set, Fuzzy set operations, Galois connection, Idempotence, Identity element, If and only if, Intersection (set theory), Involution (mathematics), Joseph Goguen, Lattice (order), Logic, Logical conjunction, Logical disjunction, Many-valued logic, Mathematics, Metric space, Monotonic function, Nilpotent, Partially ordered group, Partially ordered set, Probabilistic metric space, Probability theory, Residuated lattice, T-norm fuzzy logics, Triangle inequality, Truth value, Union (set theory), Velocity-addition formula, Zero divisor.

Archimedean property

In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields.

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Associative property

In mathematics, the associative property is a property of some binary operations.

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Łukasiewicz logic

In mathematics, Łukasiewicz logic is a non-classical, many-valued logic.

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Binary operation

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Construction of t-norms

In mathematics, t-norms are a special kind of binary operations on the real unit interval.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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De Morgan's laws

In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.

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Degree of truth

In standard mathematics, propositions can typically be considered unambiguously true or false.

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Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

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Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Fuzzy logic

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1.

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Fuzzy set

In mathematics, fuzzy sets (aka uncertain sets) are somewhat like sets whose elements have degrees of membership.

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Fuzzy set operations

A fuzzy set operation is an operation on fuzzy sets.

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Galois connection

In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).

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Idempotence

Idempotence is the property of certain operations in mathematics and computer science that they can be applied multiple times without changing the result beyond the initial application.

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Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

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Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

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Joseph Goguen

Joseph Amadee Goguen (28 June 1941 – 3 July 2006) was a US computer scientist.

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Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

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Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

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Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.

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Many-valued logic

In logic, a many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Nilpotent

In mathematics, an element, x, of a ring, R, is called nilpotent if there exists some positive integer, n, such that xn.

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Partially ordered group

In abstract algebra, a partially ordered group is a group (G,+) equipped with a partial order "≤" that is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then a+g ≤ b+g and g+a ≤ g+b.

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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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Probabilistic metric space

A probabilistic metric space is a generalization of metric spaces where the distance has no longer values in non-negative real numbers, but in distribution functions.

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Probability theory

Probability theory is the branch of mathematics concerned with probability.

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Residuated lattice

In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x ≤ y and a monoid x•y which admits operations x\z and z/y, loosely analogous to division or implication, when x•y is viewed as multiplication or conjunction, respectively.

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T-norm fuzzy logics

T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that takes the real unit interval for the system of truth values and functions called t-norms for permissible interpretations of conjunction.

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Triangle inequality

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

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Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

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Union (set theory)

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

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Velocity-addition formula

In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames.

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Zero divisor

In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero such that, or equivalently if the map from to that sends to is not injective.

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Redirects here:

S-norm, T-Norm, T-conorm, Tnorm, Triangular norm.

References

[1] https://en.wikipedia.org/wiki/T-norm

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