Institute of Information Theory and Automation

Publication details

Semigroups and triangular norms

Monography Chapter

Klement E.P., Mesiar Radko, Pap E.


serial: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, p. 63-94 , Eds: Klement E. P., Mesiar R.

publisher: Elsevier, (Amsterdam 2005)

research: CEZ:AV0Z10750506

project(s): GA402/04/1026, GA ČR

keywords: triangular norms, semigroup, subsemigroup, I-semigroup

abstract (eng):

Triangular norms turn the unit interval, equipped with the natural order, into a totally ordered semigroup with neutral element 1 and annihilator 0. After fixing the algebraic notions we study the relationship between subsemigroups and Archimedean components and triangular norms. Particular attention is paid to ordinal sums allowing new semigroups to be constructed from given ones. Another types of semigroups, the I-semigroups, is closely linked to continuous triangular norms.

abstract (cze):

Triangulárne normy robia z jednotkového intervalu (s prirodzeným usporiadaním) úplne usporiadanú pologrupu s neutrálnym prvkom 1 a anihilátorom 0. Po zavedení algebraických pojmov študujeme vzťahy medzi pologrupami, Archimedovskými komponentami a triangulárnym normami. Venujeme sa najmä ordinálnym súčtom, ktoré umožňujú konštruovať nové pologrupy z daných pologrúp. Iné typy pologrúp, konkrétne I-pologrupy, sú blizke spojitým triangulárnym normám.

Cosati: 12A

RIV: BA

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Last modification: 21.12.2012
Institute of Information Theory and Automation