الفهرس 
Introduction andPreliminariesOnly 14 pages are availabe for public view
 |  | from | 188 |  |  |
| | | from | 188 | | |
Abstract
The maincontributionofthisresearchistoestablishnewneighborhoodsusingdifferenttools
such asgraphs,roughsets,fuzzysets,andsoftsets.Thusweconstructtopologicalstructures
fromtheseneighborhoodsandstudysomeoftheirrelevanttopologicalproperties.Thenweap-
ply thesemethodstosolvereal-lifeproblemstohelpexpertsintheoperationofmakingadeci-
sion. So,thisthesisconsistsofsixchaptersthatarehighlightedasfollows.Thefirstchaptergives
a historicalbackgroundandfundamentalnotionsofroughsets,fuzzysets,softsets,topological
structures,andgraphtheory.Inthesecondchapter,weproposethreewaystostudyanddiscuss
the topologicalstructuresfromneighborhoodsystems.Thesewaysaregraph,productgraph,
and softroughsets.Weexaminesomeoftheirrelevantcharacteristics.Moreover,weusedthese
theoreticalstudiestosolvesomerealproblems.Weintroduceanotherthreetypesofnearcon-
cepts basedonanewreflexiverelationwhichisconsideredasageneralizationoftheAbo-Tabl
approaches.Weexaminetheirrelatedpropertiesandalsoexplaintherelationsbetweenthem.
Hence, werepresentanysetofelementsbyabetweennessrelation B< and studysomeoftheir
relatedcharacteristics.Thus,wedefinefourtypesofneighborhoodsfromabetweennessrelation
and usethemtoinvestigatefourtypesoftopologicalstructurescalledtopologicalbetweenness
spaces. Moreover,weconstructfourtypesofabetweennesstopologicalapproximationspacein
the thirdchapter.Themainaimofthefourthchapteristoestablishanewtypeoffuzzygraph
and illustratehowtorepresentit.Thenweconstructthedefinitionofafuzzytopologicalgraph
and investigatesomeofitsproperties.Thuswefoundoutanewwaytoprovetheisomorphism
between fuzzytopologicalgraphs.Furthermore,usingthisnewmethod,wedemonstrateanew
presentationtosmartcities.Theprimeobjectiveofthefourthchapteristointroducesometypes
of coveringmethodsbasedonfuzzysets,roughsets,andsoftsets.Thesemodelsaresoftfuzzy
roughcovering,softroughfuzzycovering,fuzzycovering,andfuzzysoftcovering.Inaddition,
we examinesomeoftheirrelevantpropertiesandwepresentsomerealapplicationsanddiscuss
them. Toprovetheeffectivenessandthereliabilityofourproposedmodels,wemadecompar-
isons betweenour’sandtheexistingmodels.Becauseoftheflowofdatainreal-life,wedecided
to workonmultigranulationratherthanonegranuleinthelastchapter.So,inthefifthchapter,we
providenewtypesofcovering-basedmulgraulationfuzzyroughsets.Also,wediscusstheirre-
lated properties.Therefore,weputforwardnumericalexamplestobesureaboutourapproaches.
Wepresentthemainobjectivesofthisstudyandpointedtheminthefinalchapter.