Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms

0411466 - UTIA-B 20050196 RIV NL eng M - Monography Chapter
Klement, E.P. - Mesiar, Radko - Pap, E.
Triangular norms: Basic notions and properties.
[Triangulárne normy: základné pojmy a vlastnosti.]
Amsterdam: Elsevier, 2005. ISBN 0-444-51814-2. In: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms. - (Klement, E.; Mesiar, R.), s. 17-62
R&D Projects: GA ČR GA402/04/1026
Institutional research plan: CEZ:AV0Z10750506
Keywords : triangular norms and conorms * additive and multiplicative generators * construction methods
Subject RIV: BA - General Mathematics

The basic definitions concerning triangular norms and conorms are collected. We also mention the most important algebraic and analytical properties a triangular norm may have. We discuss the construction of triangular norms by means of additive and multiplicative generators and via ordinal sums, and we mention also some other construction methods. Finally we present the representation theorems of continuous Archimedean triangular norms and of continuous triangular norms.

Uvádzame základné definície týkajúce sa triangulárnych noriem a konoriem. Pripomíname najdôležitejšie algebraické a analytické vlastnosti t-noriem, rozoberáme konštrukciu triangulárnych noriem pomocou aditívnych a multiplikatívnych generátorov a ordinálnych súčtov a spomíname aj niektoré ďalšie konštrukčné metódy. Záverom uvádzame reprezentačnú vetu pre spojité Archimedovské t-normy a spojité t-normy.
Permanent Link: http://hdl.handle.net/11104/0131546