About: Associativity of triangular norms characterized by the geometry of their level sets

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Associativity of triangular norms characterized by the geometry of their level sets Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Associativity of triangular norms is an algebraic property which, unlike for example their commutativity, is usually understood as hardly visually interpretable. This problem has been studied intensively in the last decade and, as a result, geometric symmetries of triangular norms with involutive level sets have been revealed. The presented paper intends to introduce a different approach which gives more general results. The inspiration is taken from web geometry, a branch of differential geometry, and its concept of Reidemeister closure condition which is known to provide a geometric characterization of associativity of loops. The paper shows that this concept can be adopted successfully for triangular norms so that it characterizes their associativity in a similar way. Moreover, the offered adaptation preserves the beneficial transparency and simplicity of the Reidemeister closure condition. This way, a visual characterization of the associativity, based on the geometry of the level sets, is provided for general, continuous, and continuous Archimedean triangular norms. Associativity of triangular norms is an algebraic property which, unlike for example their commutativity, is usually understood as hardly visually interpretable. This problem has been studied intensively in the last decade and, as a result, geometric symmetries of triangular norms with involutive level sets have been revealed. The presented paper intends to introduce a different approach which gives more general results. The inspiration is taken from web geometry, a branch of differential geometry, and its concept of Reidemeister closure condition which is known to provide a geometric characterization of associativity of loops. The paper shows that this concept can be adopted successfully for triangular norms so that it characterizes their associativity in a similar way. Moreover, the offered adaptation preserves the beneficial transparency and simplicity of the Reidemeister closure condition. This way, a visual characterization of the associativity, based on the geometry of the level sets, is provided for general, continuous, and continuous Archimedean triangular norms. (en)
Title	Associativity of triangular norms characterized by the geometry of their level sets Associativity of triangular norms characterized by the geometry of their level sets (en)
skos:prefLabel	Associativity of triangular norms characterized by the geometry of their level sets Associativity of triangular norms characterized by the geometry of their level sets (en)
skos:notation	RIV/67985807:_____/12:00381684!RIV13-GA0-67985807
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP202/10/1826)
http://linked.open...iv/cisloPeriodika	1 September
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Petrík, Milan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	123925
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/12:00381684
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	associativity; contour; level set; Reidemeister closure condition; triangular norm; web geometry (en)
http://linked.open.../riv/klicoveSlovo	contour level set Reidemeister closure condition associativity web geometry triangular norm
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[ADC59D260AAD]
http://linked.open...i/riv/nazevZdroje	Fuzzy Sets and Systems
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Matematická fuzzy logika v informatice
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	202
http://linked.open...iv/tvurceVysledku	Petrík, Milan Sarkoci, P.
http://linked.open...ain/vavai/riv/wos	000306886100006
issn	0165-0114
number of pages	10 (xsd:int)

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software