Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures

210 Pages·2020·6.749 MB·English

by  Irina Cristea (editor)

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Structures
Edited by
Irina Cristea
Printed Edition of the Special Issue Published in Symmetry
www.mdpi.com/journal/symmetry
Symmetry in Classical and Fuzzy
Algebraic Hypercompositional
Structures

Symmetry in Classical and Fuzzy
Algebraic Hypercompositional
Structures
SpecialIssueEditor
IrinaCristea
MDPI•Basel•Beijing•Wuhan•Barcelona•Belgrade•Manchester•Tokyo•Cluj•Tianjin
SpecialIssueEditor
IrinaCristea
CenterforInformation
TechnologiesandApplied
Mathematics,Universityof
NovaGorica
Slovenia
EditorialOffice
MDPI
St.Alban-Anlage66
4052Basel,Switzerland
ThisisareprintofarticlesfromtheSpecialIssuepublishedonlineintheopenaccessjournalSymmetry
(ISSN 2073-8994) (available at: https://www.mdpi.com/journal/symmetry/specialissues/Fuzzy
AlgebraicHypercompositionalStructures).
Forcitationpurposes,citeeacharticleindependentlyasindicatedonthearticlepageonlineandas
indicatedbelow:
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ISBN978-3-03928-708-6(Pbk)
ISBN978-3-03928-709-3(PDF)
(cid:2)c 2020bytheauthors. ArticlesinthisbookareOpenAccessanddistributedundertheCreative
Commons Attribution (CC BY) license, which allows users to download, copy and build upon
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Contents
AbouttheSpecialIssueEditor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Prefaceto“SymmetryinClassicalandFuzzyAlgebraicHypercompositionalStructures” . . . ix
DariushHeidariandIrinaCristea
BreakableSemihypergroups
Reprintedfrom:Symmetry2019,11,100,doi:10.3390/sym11010100 . . . . . . . . . . . . . . . . . 1
MarioDeSalvo,DarioFasino,DomenicoFreniandGiovanniLoFaro
OnHypergroupswithaβ-ClassofFiniteHeight
Reprintedfrom:Symmetry2020,12,168,doi:10.3390/sym12010168 . . . . . . . . . . . . . . . . . 11
Sˇteˇpa´nKrˇehl´ıkandJanaVyroubalova´
The Symmetry of Lower and Upper Approximations, Determined by a Cyclic Hypergroup,
ApplicableinControlTheory
Reprintedfrom:Symmetry2020,12,54,doi:10.3390/sym12010054 . . . . . . . . . . . . . . . . . . 25
VahidVahedi,MortezaJafarpourandIrinaCristea
HyperhomographiesonKrasnerHyperfields
Reprintedfrom:Symmetry2019,11,1442,doi:10.3390/sym11121442 . . . . . . . . . . . . . . . . . 41
MadelineAlTahan,SˇarkaHosˇkova-MayerovaandBijanDavvaz
SomeResultson(Generalized)FuzzyMulti-Hv-IdealsofHv-Rings
Reprintedfrom:Symmetry2019,11,1376,doi:10.3390/sym11111376 . . . . . . . . . . . . . . . . . 61
SˇarkaHosˇkova-MayerovaandBabatundeO.Onasanya
ResultsonFunctionsonDedekindMultisets
Reprintedfrom:Symmetry2019,11,1125,doi:10.3390/sym11091125 . . . . . . . . . . . . . . . . . 75
HashemBordbar,G.MuhiuddinandAbdulazizM.Alanazi
PrimenessofRelativeAnnihilatorsinBCK-Algebra
Reprintedfrom:Symmetry2020,12,286,doi:10.3390/sym12020286 . . . . . . . . . . . . . . . . . 85
XiaoLongXin,RajabAliBorzooei,MahmoodBakhshiandYoungBaeJun
IntuitionisticFuzzySoftHyperBCKAlgebras
Reprintedfrom:Symmetry2019,11,399,doi:10.3390/sym11030399 . . . . . . . . . . . . . . . . . 97
JanChvalinaandBedrˇichSmetana
SeriesofSemihypergroupsofTime-VaryingArtificialNeuronsandRelatedHyperstructures
Reprintedfrom:Symmetry2019,11,927,doi:10.3390/sym11070927 . . . . . . . . . . . . . . . . . 109
MichalNova´k,Sˇtepa´nKrˇehl´ıkandKyriakosOvaliadis
ElementsofHyperstructureTheoryinUWSNDesignandDataAggregation
Reprintedfrom:Symmetry2019,11,734,doi:10.3390/sym11060734 . . . . . . . . . . . . . . . . . 121
AnamLuqman,MuhammadAkramandAliN.A.Koam
Anm-PolarFuzzyHypergraphModelofGranularComputing
Reprintedfrom:Symmetry2019,11,483,doi:10.3390/sym11040483 . . . . . . . . . . . . . . . . . 137
MuhammadAkram,AmnaHabibandAliN.A.Koam
ANovelDescriptiononEdge-Regularq-RungPictureFuzzyGraphswithApplication
Reprintedfrom:Symmetry2019,11,489,doi:10.3390/sym11040489 . . . . . . . . . . . . . . . . . 159
v

About the Special Issue Editor
Irina Cristea received her Ph.D. degree in mathematics in 2007 from University Ovidius of
Constanta,Romania. AfteraperiodofpostdoctoratestudiesatUniversityofUdine,Italy,in2012,
shebecameAssistantProfessorattheUniversityofNovaGorica,Slovenia,whereshecurrentlyhold
thepositionofAssociateProfessorandactingheadoftheCenterforInformationTechnologiesand
AppliedMathematics.
Her main research direction is theory of algebraic hypercompositional structures and their
connectionswithfuzzysetstheory. Inthisarea,shehaspublishedmorethan60reasearcharticles
injournalsindexedbyScopus/WebofScience. Sheisalsoaco-authorofthemonograph“Fuzzy
AlgebraicHyperstructures:AnIntroduction”publishedin2015bySpringer.
Prof. IrinaCristeaisdeeplyinvolvedintheeditorialactivities,beingmemberoftheEditorial
Boardoffiveinternationaljournals(amongthemMathematics,publishedbyMDPI)andactingas
areviewerfornumerousjournals. In2019,shewasawardedbyPublonsthe“Top1%Reviewersin
Mathematics”.
vii

Preface to “Symmetry in Classical and Fuzzy
Algebraic Hypercompositional Structures”
Symmetryplaysafundamentalroleinourdailylivesandinthestudyofthestructureofdifferent
objectsinphysics,chemistry,biology,mathematics,architecture,arts,sociology,linguistics,etc. For
example, the structureof moleculesis wellexplained bytheir symmetry properties, described by
symmetryelementsandsymmetryoperations. Asymmetryoperationisachange,atransformation
afterwhichcertainobjectsremaininvariant,suchasrotations,reflections,inversions,orpermutation
operations.Untilnow,themostefficientmethodtobetterdescribesymmetrywasusingmathematical
toolsofferedbygrouptheory.
Naturally generalizing the concept of a group, by considering the result of the interaction
between two elements of a non-empty set to be a set of elements (and not only one element, as
for groups), Frederic Marty, in 1934, at only 23 years old, defined the concept of a hypergroup.
The law characterizing such a structure is called multi-valued operation, hyperoperation, or
hypercomposition,andthetheoryofthealgebraicstructuresendowedwithatleastonemulti-valued
operation is known as hyperstructure theory or hypercompositional algebra. Marty’s motivation
tointroducehypergroupswasthatthequotientofagroupmoduloanysubgroup(notnecessarily
normal)isahypergroup.
ThemainaimofthisSpecialIssuewastopresentrecentadvancesinhypercompositionalalgebra,
thecrispandfuzzyalgebra,wheresymmetryplaysacrucialrole.Studiesarerelated(butnotlimited)
to equivalence relations, orderings, permutations, symmetrical groups, graphs and hypergraphs,
lattices,fuzzysets,representations,etc.Someapplicationsofalgebraichypercompositionalstructures
in engineering, information technologies, computer science, where symmetry, or the lack of
symmetry,isclearlyspecifiedandlaidout,arealsounderlined.
IrinaCristea
SpecialIssueEditor
ix