语言真值概念格及其应用（英文版）

Contents

Preface

Chapter 1 Introduction 1

1.1 Basic Academic Ideas 1

1.2 Classical Concept Lattice 2

1.3 Fuzzy Concept Lattice 4

1.4 Lattice-Valued Logic and Lattice Implication Algebra 6

1.5 Status of Concept Lattice 9

Chapter 2 Linguistic Truth-Valued Concept Lattice 15

2.1 Introduction 15

2.2 Linguistic Truth-Valued Lattice Implication Algebra 16

2.3 Linguistic Truth-Valued Concept Lattice 27

2.4 Matrix Constructing Method of Linguistic Truth-Valued Concept Lattice 30

Chapter 3 Reduction Methods of Linguistic Truth-Valued Concept Lattice 43

3.1 Introduction 43

3.2 Attribute Reduction of Linguistic Truth-Valued Concept Lattice 44

3.3 Object Reduction of Linguistic Truth-Valued Concept Lattice 49

Chapter 4 Distributed Computing and Parallel Processing of Linguistic Truth-Valued Concept Lattice 55

4.1 Introduction 55

4.2 Representation Algorithm of Extended Linguistic Truth-Valued Formal Context 56

4.3 Decomposition Operation of Linguistic Truth-Valued Concept Lattice 65

4.4 Combination Operation of Linguistic Truth-Valued Concept Lattice 73

Chapter 5 Uncertainty Reasoning Based on Linguistic Truth-Valued Concept Lattice 85

5.1 Introduction 85

5.2 Internal Approximate Uncertainty Reasoning Method Based on Linguistic Truth-Valued Concept Lattice 87

5.3 External Approximate Uncertainty Reasoning Method Based on Linguistic Truth-Valued Concept Lattice 93

5.4 Relationship Between the Internal and External Approximate Uncertainty Reasoning Methods 99

Chapter 6 Decision Making Based on Linguistic Truth-Valued Concept Lattice 111

6.1 Introduction 111

6.2 Multi-Target Decision Model Based on Linguistic Truth-Valued Concept Lattice 113

6.3 Single-target Decision Model Based on Linguistic Truth-Valued Concept Lattice 127

6.4 The Application of Linguistic Truth-Valued Concept Lattice 139

References 147