粗糙集理论及其应用研究

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1、代号⋯⋯⋯_19婴王⋯⋯⋯分类号⋯⋯⋯一艘堡⋯⋯⋯学号⋯⋯⋯02⋯031⋯10⋯004⋯⋯一密级⋯⋯⋯。公珏⋯⋯⋯．蚤簧它争释虢磊警博士学位论文《≯驾》，瞄善?毫√兰≯、，

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4、≮jj。鎏毒；岭遴澎曩爹～／一题(中、英文)目粗糙集理论及其应用研究⋯⋯⋯⋯⋯⋯⋯⋯一⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯-StudyonRoughSets⋯⋯⋯⋯⋯⋯⋯一⋯一一-⋯一⋯⋯⋯⋯⋯⋯一⋯⋯⋯一⋯⋯●-一TheoryanditsApplications作者姓名王珏指导教师姓名、职务刘三阳教授学科门类理学学科、专业应用数学⋯⋯⋯⋯一一⋯⋯一⋯⋯⋯●⋯⋯一⋯⋯⋯

5、⋯一⋯一提交论文日期二0o五年四月vague集的模糊多属性决策问题，即方案关于属性的取值是vague值的多属性决策问题。利用评分函数构造了vague正理想解和vague负理想解，定义了vague值之间的加权距离测度，通过计算方案与理想解2_N的距离，得出每个方案的贴近度，最后依照贴近度对方案集进行排序，选出最优方案。关键词：粗糙集vague集相容粗糙集模糊粗糙集优势粗糙集属性约简决策规则和谐关系群决策模糊多准则决策TOPSIS信息检索ABSTRACTRoughsettheory,initializedbyProfessorPawlakinearly1

6、980’S，hasbeenprovedtobeanexcellentmathematicaltooldealingwithuncertainandvaguedescriptionofobjects，whosebasicideaistoderiveclassificationrolesofconceptionbyknowledgereductionwiththeabilityofclassificationunchanged．Itcanfindthehidingandpotentialrules，thatisknowledge，fromthedataw

7、ithoutanypreliminaryoradditionalinformation．Inrecentyears，asailimportantpartofsoftcomputing，roughsettheoryhasbeenwidelyusedinmanyareas，especiallyintheareaofpattemrecognition，machinelearning，decisionanalysis，knowledgediscoveryandknowledgeacquisitionetc．Inthisdissertation，thefocu

8、sisonroughsetstheoryandvaguesetstheorywiththeirapplicationsingroupdecisionmakingproblems，informationretrievalandfuzzymulti-criteriadecisionmakingproblems．Themaincontributionsandoriginalideasincludedinthedissertationaresummarizedasfollows．1．Anoveldefinitionofentropyisintroducedf

9、ortolerantroughsettheory,onthebasisofwhichtherelationbetweenknowledgeandentropyisconstructed．Weprovethattheentropyofknowledgedecreasesmonotonouslyasthegranularityofinformationbecomessmaller．Thenanewreductionalgorithmintolerantroughsetispresented．Anotherattributereductionalgorit

10、hmisdevelopedforageneraltypeoffuzzydatabyusingaresemblancerelationbasedonpseudometric．Anovelroughsetmodelbasedonconcordancerelationispresented，whichrelaxingtheindiscernibilityandtolerancebetweenobjectsonthebasisofclassicalandtolerantroughsets．Wemakeananalysisoftherelationbetwee

11、nroughnessofconcordancerelationmadentropy，Anexampleiss