基於商空間的問題求解(Quotient Space Based Problem Solving)

基本信息

基於商空間的問題求解（Quotient Space Based Problem Solving）
作者：張鈴、張鈸

ISBN：9787302384953
定價：120元
印次：1-1
裝幀：精裝
印刷日期：2014-12-8

圖書簡介

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