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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F12%3A00381684" target="_blank" >RIV/67985807:_____/12:00381684 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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, andits 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

Název v anglickém jazyce

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

Popis výsledku anglicky

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, andits 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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Matematická fuzzy logika v informatice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

202

Číslo periodika v rámci svazku

1 September

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

10

Strana od-do

100-109

Kód UT WoS článku

000306886100006

EID výsledku v databázi Scopus

—