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Publication details

Triangular norms: Basic notions and properties

Monography Chapter

Klement E.P., Mesiar Radko, Pap E.


serial: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, p. 17-62 , Eds: Klement E. P., Mesiar R.

publisher: Elsevier, (Amsterdam 2005)

research: CEZ:AV0Z10750506

project(s): GA402/04/1026, GA ČR

keywords: triangular norms and conorms, additive and multiplicative generators, construction methods

abstract (eng):

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.

abstract (cze):

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.

Cosati: 12A

RIV: BA

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Last modification: 21.12.2012
Institute of Information Theory and Automation