الفهرس | Only 14 pages are availabe for public view |
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. |