Publication result detail

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

CRISTEA, I.; KOCIJAN, J.; NOVÁK, M.

Original Title

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

English Title

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

Type

WoS Article

Original Abstract

The aim of this paper is to study, from an algebraic point of view, the properties of interdependencies between sets of elements (i.e., pieces of secrets, atmospheric variables, etc.) that appear in various natural models, by using the algebraic hyperstructure theory. Starting from specific examples, we first define the relation of dependence and study its properties, and then, we construct various hyperoperations based on this relation. We prove that two of the associated hypergroupoids are Hv-groups, while the other two are, in some particular cases, only partial hypergroupoids. Besides, the extensivity and idempotence property are studied and related to the cyclicity. The second goal of our paper is to provide a new interpretation of the dependence relation by using elements of the theory of algebraic hyperstructures.

English abstract

The aim of this paper is to study, from an algebraic point of view, the properties of interdependencies between sets of elements (i.e., pieces of secrets, atmospheric variables, etc.) that appear in various natural models, by using the algebraic hyperstructure theory. Starting from specific examples, we first define the relation of dependence and study its properties, and then, we construct various hyperoperations based on this relation. We prove that two of the associated hypergroupoids are Hv-groups, while the other two are, in some particular cases, only partial hypergroupoids. Besides, the extensivity and idempotence property are studied and related to the cyclicity. The second goal of our paper is to provide a new interpretation of the dependence relation by using elements of the theory of algebraic hyperstructures.

Keywords

hyperoperation; hypergroupoid; dependence relation; influence; impact

Key words in English

hyperoperation; hypergroupoid; dependence relation; influence; impact

Authors

CRISTEA, I.; KOCIJAN, J.; NOVÁK, M.

RIV year

2020

Released

23.09.2019

Publisher

MDPI

ISBN

2227-7390

Periodical

Mathematics

Volume

7

Number

10

State

Swiss Confederation

Pages from

1

Pages to

4

Pages count

14

URL

https://www.mdpi.com/2227-7390/7/10/885

Full text in the Digital Library

http://hdl.handle.net/11012/188981

BibTex

@article{BUT158840,
  author="Irina {Cristea} and Juš {Kocijan} and Michal {Novák}",
  title="Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures",
  journal="Mathematics",
  year="2019",
  volume="7",
  number="10",
  pages="1--4",
  doi="10.3390/math7100885",
  url="https://www.mdpi.com/2227-7390/7/10/885"
}

Documents

mathematics-07-00885-v2