基本介紹
- 書名：基於商空間的問題求解(Quotient Space Based Problem Solving)
- 作者：張鈴、張鈸
- 出版社：清華大學出版社
- 出版時間：2014年10月8日
- 定價：120 元
- 裝幀：精裝
- ISBN：9787302384953
- 印刷日期：2014-12-8
內容簡介,目錄,
內容簡介
本書針對人類問題求解的特點建立一個基於商空間的數學模型，這個模型也是分層多粒度計算的理論基礎。該理論能有效地解析目前已有的多粒度分析方法，如小波分析、分形幾何和模糊集理論等；不僅適用於以問題求解為代表的人類深思熟慮的行為，同時也適用於人類的感知，如視覺信息處理等。
本書共分7章和2個附錄。第1章講述問題的描述方法，關鍵是不同粒度世界的描述。第2章講述分層與多粒度計算，重點是其數學模型，多粒度計算與計算複雜性、模糊分析的關係，以及它的套用。第3章多粒度計算中信息合成的數學模型，並由此導出合成的原則和方 法。第4章多粒度世界中的推理，包括推理模型，不確定性與粒度的關係，推理網路、定性推理與模糊推理等。第5章自動空間規劃，包括裝配序列的自動產生，運動規劃中的幾何與拓撲方法，降維法及其套用。第6章介紹統計啟發式搜尋方法，分析它的理論、計算複雜性、算法的實現，這種算法的特點及其與多粒度計算的關係。第7章商空間問題求解理論的推廣，包括將理論推廣到非等價關係，該理論與小波分析與分形幾何的關係，以及在系統分析中的套用。最後，在附錄中介紹若干與本書內容關係密切的數學內容，主要是統計推斷與點集拓撲的某些概念和結論，供不熟悉這部分數學內容的讀者閱讀時參考。
本書是從事計算機、人工智慧、模式識別以及粒計算等領域的科學工作者的有益參考書。
目錄
Contents
Preface....................................................vii
Chapter1ProblemRepresentations....................................1
1.1.ProblemSolving.............................................1
1.1.1.ExpertConsultingSystems...................................2
1.1.2.TheoremProving..........................................2
1.1.3.AutomaticProgramming.....................................2
1.1.4.GraphicalRepresentation.....................................3
1.1.5.AND/ORGraphicalRepresentation.............................3
1.2.WorldRepresentationsatDifferentGranularities......................5
1.2.1.TheModelofDifferentGrain-SizeWorlds........................5
1.2.2.TheDe.nitionofQuotientSpace...............................7
1.3.TheAcquisitionofDifferentGrain-SizeWorlds......................8
1.3.1.TheGranulationofDomain...................................8
1.3.2.TheGranulationbyAttributes.................................9
1.3.3.GranulationbyStructures...................................11
1.4.TheRelationAmongDifferentGrainSizeWorlds....................13
1.4.1.TheStructureofMulti-GranularWorlds.........................13
1.4.2.TheStructuralCompletenessofMulti-GranularWorlds.............15
1.5.Property-PreservingAbility....................................21
1.5.1.Falsity-PreservingPrinciple..................................21
1.5.2.QuotientStructure.........................................32
1.6.SelectionandAdjustmentofGrain-Sizes..........................32
1.6.1.MergenceMethods........................................33
Example1.15.................................................34
1.6.2.DecompositionMethods....................................34
1.6.3.TheExistenceandUniquenessofQuotientSemi-Order.........................41
1.6.4.TheGeometricalInterpretationofMergenceandDecompositionMethods...................42
1.7.Conclusions................................................43
Chapter2HierarchyandMulti-GranularComputing.......................45
2.1.TheHierarchicalModel.......................................45
2.2.TheEstimationofComputationalComplexity.......................48
2.2.1.TheAssumptions.........................................48
2.2.2.TheEstimationoftheComplexityUnderDeterministicModels.....................49
2.2.3.TheEstimationoftheComplexityUnderProbabilisticModels........54
2.3.TheExtractionofInformationonCoarselyGranularLevels.............62
2.3.1.Examples...............................................64
2.3.2.Constructing[f]UnderUnstructuredDomains....................65
2.3.3.Constructing[f]UnderStructuredDomains......................67
2.3.4.Conclusions.............................................77
2.4.FuzzyEquivalenceRelationandHierarchy.........................77
2.4.1.ThePropertiesofFuzzyEquivalenceRelations....................77
2.4.2.TheStructureofFuzzyQuotientSpaces.........................84
2.4.3.ClusterandHierarchicalStructure.............................86
2.4.4.Conclusions.............................................88
2.5.TheApplicationsofQuotientSpaceTheory........................88
2.5.1.Introduction.............................................88
2.5.2.TheStructuralDe.nitionofFuzzySets.........................90
2.5.3.TheRobustnessoftheStructuralDe.nitionofFuzzySets............95
2.5.4.Conclusions............................................102
2.6.Conclusions...............................................102
Chapter3InformationSynthesisinMulti-GranularComputing...............105
3.1.Introduction...............................................105
3.2.TheMathematicalModelofInformationSynthesis..................106
3.3.TheSynthesisofDomains....................................108
3.4.TheSynthesisofTopologicStructures...........................109
3.5.TheSynthesisofSemi-OrderStructures..........................110
3.5.1.TheGraphicalConstructingMethodofQuotientSemi-Order........110
3.5.2.TheSynthesisofSemi-OrderStructures............112
3.6.TheSynthesisofAttributeFunctions..............117
3.6.1.TheSyntheticPrincipleofAttributeFunctions ...117
3.6.2.Examples......................120
3.6.3.Conclusions....................126
Chapter4ReasoninginMulti-GranularWorlds...............129
4.1.ReasoningModels...............129
4.2.TheRelationBetweenUncertaintyandGranularity ....133
4.3.Reasoning(Inference)Networks(1)...............135
4.3.1.Projection..........138
4.3.2.Synthesis...........140
4.3.3.ExperimentalResults..........146
4.4.ReasoningNetworks(2)..............147
4.4.1.Modeling..................151
4.4.2.TheProjectionofAND/ORRelations..........152
4.4.3.TheSynthesisofAND/ORRelations..........155
4.4.4.Conclusion..............160
4.5.OperationsandQuotientStructures...........160
4.5.1.TheExistenceofQuotientOperations...........162
4.5.2.TheConstructionofQuotientOperations...........164
4.5.3.TheApproximationofQuotientOperations.............172
4.5.4.ConstraintsandQuotientConstraints............176
4.6.QualitativeReasoning.............181
4.6.1.QualitativeReasoningModels.............182
4.6.2.Examples.............182
4.6.3.TheProcedureofQualitativeReasoning.........186
4.7.FuzzyReasoningBasedonQuotientSpaceStructures ...187
4.7.1.FuzzySetBasedonQuotientSpaceModel.........187
4.7.2.Fuzzi.edQuotientSpaceTheory................189
4.7.3.TheTransformationofThreeDifferentGranularComputingMethods.......190
4.7.4.TheTransformationofProbabilisticReasoningModels.............191
4.7.5.Conclusions............191
Chapter5AutomaticSpatialPlanning.................193
5.1.AutomaticGenerationofAssemblySequences..........194
5.1.1.Introduction............194
5.1.2.Algorithms............195
5.1.3.Examples...........199
5.1.4.ComputationalComplexity..............202
5.1.5.Conclusions..........204
5.2.TheGeometricalMethodsofMotionPlanning...........205
5.2.1.Con.gurationSpaceRepresentation..........205
5.2.2.FindingCollision-FreePaths...........206
5.3.TheTopologicalModelofMotionPlanning...........207
5.3.1.TheMathematicalModelofTopology-BasedProblemSolving. ..208
5.3.2.TheTopologicModelofCollision-FreePathsPlanning. ....210
5.4.DimensionReductionMethod...........216
5.4.1.BasicPrinciple........................216
5.4.2.CharacteristicNetwork....................221
5.5.Applications...................230
5.5.1.TheCollision-FreePathsPlanningforaPlanarRod.... ...231
5.5.2.MotionPlanningforaMulti-JointArm..............237
5.5.3.TheApplicationsofMulti-GranularComputing............242
5.5.4.TheEstimationoftheComputationalComplexity........246
Chapter6StatisticalHeuristicSearch.................249
6.1.StatisticalHeuristicSearch..............251
6.1.1.HeuristicSearchMethods..............251
6.1.2. StatisticalInference.......................................254
6.1.3. StatisticalHeuristicSearch .................................256
6.2. TheComputationalComplexity ................................259
6.2.1. SPA Algorithms .........................................259
6.2.2. SAA Algorithms .........................................262
6.2.3. Different Kinds of SA ... .... .... .... .... .... .... .... ... ...264
