粗糙集理论及其在多目标优化中的应用

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1、西安电子科技大学博士学位论文粗糙集理论及其在多目标优化中的应用姓名：邓方安申请学位级别：博士专业：应用数学指导教师：刘三阳20021201集、冲突解集等概念．通过计算各个目标函数支持解集、中立解集、冲突解集，不仅可以确定目标函数之间的相互关系，而且可以对参考解进行排序．利用属性约简可以确定多目标优化问题中的核心目标函数，为决策者提供更为可靠的决策信息．关键词：粗糙集上、下近似算子分配Bz一格模式分类可能性测度必然性测度约束度多目标规划冲突分析ABSTRACTRoughSetTheory,introducedbyZ．Pawlak1980’s(Pawlak，1991；Pawlaketa1．，199

2、5)，isanewmathematicaltooltOdealwithvaguenessanduncertainty．Morerecentlv，asanimportantmethodfortllesoftcomputingininformationscience．roll【ghsettheoryhasbecomeoneofthemostactiveresearchfieldofartificialintelligenceandinformationscience，andithasbeensuccessfullyappliedtomanyareassuchaspattemrecognition，

3、conflictanalysis，datamining，intelligentcontrol，machinelearning，knowledgeacquisition，medicinediagnosis，expertsystems，artificialneuralnetworks，decisionanalysis，knowledgediscoyeryfromdatabases，machinediagnosis，materialscience，financialandmarketanalysis，andSOon．Roughsettheoryanditsapplicationsinmultiple

4、objectiveoptimizationsarestudiedinthispaper．ItisouraimstofindnewapproachestosolvemultipleobjectiveoptimizationproblemandtOinitiatenewareasofroughSet．Detailasfollows：1．TherelationshipbetweenroughsetsandintervalstructureofthedistributiveBZ·latticesisdiscussed，Westudytheintervalstructureandpropertiesof

5、thedistributiveBZ-lattieesandconstructaroughsetalgebraoverthem．Inaddition，apairofdualoperatorsisconstructedbyusinganti-intuitionoperatorsovertlledistributiveBZ—lattices．whichnotonlyhasexcellentpropertiesbutalsogeneratesaroughsetalgebraItisprovedthattheroughsetapproximation(V(口)，“(口))ofanyaindistribu

6、tiveBZ-latticesCanbeinducedfromtwomodal-likeunaryoperators(vfornecessityand”forpossibility)，SOCanaroughsetalgebraforanygivendistributiveBZ-lattice．2．Thepropertiesofroughapproximationoperatorsbasedonthebisectionmethodofpattemarestudied，Wedescribethepossibilityandnecessityofpatternclassificationbydivi

7、dingapatternspaceintotwodecisionareas，thenanewroughneuralnetworksalgorithmofpossibilityandnecessityoftheclassificationproblemwithboundaryareasisdesigned．Anexampleshowsthatthealgorithmiseffective．The“l