Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups

Reference : Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups


	Document type :	Parts of books : Contribution to collective works
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/31497

Title :	Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups
Language :	English
Author, co-author :	Kiss, Gergely [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Somlai, Gabor []
Publication date :	Jun-2017
Main document title :	Aggregation Functions in Theory and in Practice
Author, co-author :	Torra, Vicenç
	Mesiar, Radko
	De Baets, Bernard
Publisher :	Springer
Peer reviewed :	Yes
Abstract :	[en] We investigate n-ary semigroups as a natural generalization of binary semigroups. We refer it as a pair (X,F_n), where X is a set and an n-associative function F_n : X^n -> X is defined on X. We show that if F_n is idempotent, n-associative function which is monotone in each of its variables, defined on an interval I and has a neutral element, then F_n is combination of the minimum and maximum operation. Moreover we can characterize the n-ary semigroups (I,F_n) where F_n has the previous properties.
Permalink :	http://hdl.handle.net/10993/31497

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Open access	AGOP2017Kiss.pdf		Publisher postprint	584.79 kB	View/Open

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Open access	Kiss-Somlai_revised.pdf		136.68 kB	View/Open

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