粗糙集理論在代數(shù)系統(tǒng)——群、環(huán)上的應(yīng)用.pdf

1、電子科技大學碩士學位論文粗糙集理論在代數(shù)系統(tǒng)——群、環(huán)上的應(yīng)用姓名：王德松申請學位級別：碩士專業(yè)：運籌學與控制論指導教師：舒蘭20030101AbstractRoughsettheoryisnotonlyanewmathematicaltooldealingwithvaguenessanduncertaintybutalsoanewandeffectivesoftcomputingmethodItwasbeenwidelyusedint

2、heareaofmachinelearning，knowledgediscoverydecisionanalysis，artificialintelligence，datamining，patternrecognition，faultdiagnosis，etcAtthesanletime，somearticlesthathavebeenstudiedaboutthetheorycombinedpuremathematicswithrou

3、ghsetshavebeenemerged，andsomenewmathematicalnotions，suchasroughlogic，roughidealinsemigroups，roughgroupsandroughsubgroups，roughcosets，roughinvafiantsubgroupsandhomomorphismandisomorphismofroughgroups，areintroducedCertainl

4、ywiththeintegrationofroughstructureandalgebrastructure，topologystructure，orderstructuremadtheotherstructures，somenewvitalmathematicalbrancheswillbeemergedAccordingtotheroughstructureandalgebrastructure，themainworkistostu

5、dytheapplicationofroughsettheoryonalgebrasystemgroupsandringsinthisthesisSothatroughalgebrasystemisbuiltbetterperfectlyThegeneralprocessasfollows：1ThemainworkistostudytheapplicationofroughsettheoryonalgebrasystemgroupsFi

6、rstlythedefinitionandpropertiesofroughsemigroupsisgivenThensomepropertiesofroughsubgroupsbasedonroughgroupsandroughsubgroupsareintroduced，andthreeimportantpropertiesofroughinvariantsubgroupsandtheconceptofroughquotientgr

7、oupsbasedonroughcosetsandroughinvariantsubgroupsareintroducedSubsequentlybasedOilsomeconceptsofhomomorphismandisomorphismofroughgroups，basichomomorphismtheoremandisomorphismtheoremofroughgroupsareputforwardandproved2Them

8、ainworkistostudytheapplicationofroughsettheoryonalgebrasystemringsFirstly，thedefinitionandpropertiesofroughringsisgivenThenthedefinitionandpropertiesofroughsubrings，roughidealandroughquotientringsareputforwardandprovedFi

9、nallyhomomorphismandisomorphismofroughringsisstudiedTherearefourchaptersinthisthesis：Inchapter1，presentstateofresearchesmaddevelopmentprosperityoftheroughsettheoryareintroducedInchapter2，basicknowledgeoftheroughsettheory