Reference : Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups
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Physical, chemical, mathematical & earth Sciences : Mathematics
Generalization of Czoga\l a-Drewniak Theorem for $n$-ary semigroups
Kiss, Gergely mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Somlai, Gabor []
Aggregation Functions in Theory and in Practice
Torra, Vicenç
Mesiar, Radko
De Baets, Bernard
[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.

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