Cyclicity in EL–Hypergroups

Novák, Michal; Křehlík, Štěpán; Cristea, Irina

doi:10.3390/sym10110611

Cited by 14 publications

(13 citation statements)

References 15 publications

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“…Now we will present an example of an infinite hypergroup and study its fuzzy reducibility. [17]. Define now on Z the fuzzy set µ as follows: µ(0) = 0 and µ(x) = 1 |x| , for any x = 0.…”

Section: Remark 2 (I)mentioning

confidence: 99%

Fuzzy Reduced Hypergroups

Kankaraš

Cristea

2020

Mathematics

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The fuzzyfication of hypercompositional structures has developed in several directions. In this note we follow one direction and extend the classical concept of reducibility in hypergroups to the fuzzy case. In particular we define and study the fuzzy reduced hypergroups. New fundamental relations are defined on a crisp hypergroup endowed with a fuzzy set, that lead to the concept of fuzzy reduced hypergroup. This is a hypergroup in which the equivalence class of any element, with respect to a determined fuzzy set, is a singleton. The most well known fuzzy set considered on a hypergroup is the grade fuzzy set, used for the study of the fuzzy grade of a hypergroup. Based on this, in the second part of the paper, we study the fuzzy reducibility of some particular classes of crisp hypergroups with respect to the grade fuzzy set.

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“…Now we will present an example of an infinite hypergroup and study its fuzzy reducibility. [17]. Define now on Z the fuzzy set µ as follows: µ(0) = 0 and µ(x) = 1 |x| , for any x = 0.…”

Section: Remark 2 (I)mentioning

confidence: 99%

Fuzzy Reduced Hypergroups

Kankaraš

Cristea

2020

Mathematics

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“…It is to be noted that, since the class of EL-hyperstructures is rather broad, the aim of many theorems included in some of those papers was to establish a common ground for some already existing ad hoc derived results. Recently, some examples concerning various types of cyclicity in hypergroups have been constructed using EL-hyperstructures, see Novák, Křehlík and Cristea [23].…”

Section: Mathematical Background Of the Modelmentioning

confidence: 99%

Elements of Hyperstructure Theory in UWSN Design and Data Aggregation

2019

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In our paper we discuss how elements of algebraic hyperstructure theory can be used in the context of underwater wireless sensor networks (UWSN). We present a mathematical model which makes use of the fact that when deploying nodes or operating the network we, from the mathematical point of view, regard an operation (or a hyperoperation) and a binary relation. In this part of the paper we relate our context to already existing topics of the algebraic hyperstructure theory such as quasi-order hypergroups, E L -hyperstructures, or ordered hyperstructures. Furthermore, we make use of the theory of quasi-automata (or rather, semiautomata) to relate the process of UWSN data aggregation to the existing algebraic theory of quasi-automata and their hyperstructure generalization. We show that the process of data aggregation can be seen as an automaton, or rather its hyperstructure generalization, with states representing stages of the data aggregation process of cluster protocols and describing available/used memory capacity of the network.

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“…A hyperoperation "•" on a nonempty set S, satisfying the property x, y ∈ x • y for all elements x, y ∈ S, is called extensive (by J. Chvalina and his group of researchers [13][14][15]) or closed (by Ch. Massouros [16]).…”

Section: Definition 3 a Semihypergroup S Is Called Breakable If Evermentioning

confidence: 99%

Breakable Semihypergroups

Heidari¹,

Cristea

2019

Symmetry

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In this paper, we introduce and characterize the breakable semihypergroups, a natural generalization of breakable semigroups, defined by a simple property: every nonempty subset of them is a subsemihypergroup. Then, we present and discuss on an extended version of Rédei’s theorem for semi-symmetric breakable semihypergroups, proposing a different proof that improves also the theorem in the classical case of breakable semigroups.

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Cyclicity in EL–Hypergroups

Cited by 14 publications

References 15 publications

Fuzzy Reduced Hypergroups

Fuzzy Reduced Hypergroups

Elements of Hyperstructure Theory in UWSN Design and Data Aggregation

Breakable Semihypergroups

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