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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. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of…

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Overview

Definition

Prominent examples

Properties of t-norms

Residuum

T-conorms

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Map overview Semantic statistics

T-norm

Nodes56
Edges55
Triples70
Avg. degree1.96
Density0.035714
Components1

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T-norm

Top relations

related to References · 30
T-norm → Acta Polytechnica Hungarica, Algebraic Foundations, An, D'Ottaviano, Daniele, Dordrecht, Endre, Erich Peter, Fuzzy Logic, Hájek, ISBN, ISSN, Itala, János, Klement, Kluwer, Left-continuous, Lock-gray-alt-2, Lock-green, Lock-red-alt-2
related to Prominent examples · 6
T-norm → Archimedean, Besides, Gödel, It, Minimum, Product
is a · 5
T-norm → function T, pointwise smallest t-norm, pointwise smallest t-norm and the minimum is the pointwise largest t-norm, standard semantics for strong conjunction in product fuzzy logic, standard semantics for strong conjunction in Łukasiewicz fuzzy logic
related to T-conorms · 5
T-norm → De Morgan's, Given, S-norms, T-conorms, This
related to Examples of t-conorms · 4
T-norm → Gödel, Important, It, Maximum
related to Residuum · 4
T-norm → For, In, Rightarrow, This
related to Basic properties of residua · 3
T-norm → Consequently, If, Rightarrow
related to Definition · 3
T-norm → Commutativity, Monotonicity, The
related to Properties of continuous t-norms · 3
T-norm → Although, Analogous, Archimedean
related to Properties of t-conorms · 3
T-norm → Dually, For, Many

Important terminology Word statistics

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Important terminology

displaystyle t-norms continuous fuzzy nilpotent logic called standard product also interval semantics residuum conjunction archimedean top łukasiewicz t-conorms element strong

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
T-normis afunction T0.90text
T-normis astandard semantics for strong conjunction in product fuzzy logic0.90text
T-normis astandard semantics for strong conjunction in Łukasiewicz fuzzy logic0.90text
T-normis apointwise smallest t-norm0.90text
T-normis apointwise smallest t-norm and the minimum is the pointwise largest t-norm0.90text
T-normrelated to Basic properties of residuaIf0.60section
T-normrelated to Basic properties of residuaRightarrow0.60section
T-normrelated to Basic properties of residuaConsequently0.60section
T-normrelated to Classification of t-normsSimilarly0.60section
T-normrelated to DefinitionCommutativity0.60section
T-normrelated to DefinitionMonotonicity0.60section
T-normrelated to DefinitionThe0.60section

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