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

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Associativity of triangular norms characterized by the geometry of their level sets
Original language 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, 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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Mathematical Fuzzy Logic in Computer Science</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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