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

Parts of books : Contribution to collective works | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/31497 | |||

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

English | |

Kiss, Gergely [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Somlai, Gabor [] | |

Jun-2017 | |

Aggregation Functions in Theory and in Practice | |

Torra, VicenĂ§ | |

Mesiar, Radko | |

De Baets, Bernard | |

Springer | |

Yes | |

[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. | |

http://hdl.handle.net/10993/31497 |

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