声明
摘要
Abstract
Symbols and Abbreviations
Chapter 1 Introduction
1．1 Research motivation
1．1．1 General background
1．1．2 Related work
1．1．3 Objectives and problem descriptions
1．2 Contributions
1．3 Organization of the dissertation
Chapter 2 Basic definitions and properties
2．1 Triangular norms and fuzzy negation
2．2 Fuzzy equivalence
2．3 Implication functions
Chapter 3 Some new approaches to constructing similarity measures
3．1 Introduction
3．2 Generating fuzzy equivaleneies
3．2．1 Fuzzy equivalencies based on biresiduation
3．2．2 Fuzzy equivalencies based on fuzzy connectives
3．3 Constructing similarity measures via fuzzy equivalencies
3．4 A comparison of properties of similarity measures
3．5 Discussion
Chapter 4 Some new approaches to constructing similarity measures of interval-valued fuzzy sets
4．1 Introduction
4．2 Constructing similarity measures of IVFSs
4．2．1 The concept ofsimilarity measures of IVFSs
4．2．2 Approaches to constructing similarity measures of IVFSs
4．3 Properties of similarity measures of IVFSs
4．4 Discussion
Chapter 5 Relations among similarity measure and other fuzzy measures
5．1 Introduction
5．2 Relations among similarity measure and divergence measure
5．2．1 Generating dissimilarity functions
5．2．2 Two methods of construction of divergence measures
5．2．3 Some properties of divergence measures
5．3 Relations among similarity measure，subsethood measure and fuzzy entropy
5．3．1 Relation between similarity measure and subsethood measure
5．3．2 Relation between similarity measure and fuzzy entropy
5．3．3 Relation between subsethood measure and fuzzy entropy
5．4 Discussions
Chapter 6 Similarity-based approximate reasoning method
6．1 Introduction
6．2 Two approaches to similarity-based approximate reasoning
6．2．1 Raha’s approach to similarity-based approximate reasoning
6．2．2 Feng’s approach to similarity-based approximate reasoning
6．3 Several properties of Raha’s similarity-based approximate reasoning method
6．3．1 The relationships among the four inferred conclusions
6．3．2 The monotonicity of Raha’s similarity-based approximate reasoning method
6．3．3 The approximation property of Raha’s similarity-based approximate reasoning method
6．4 Discussions
Chapter 7 Robustness of fuzzy connectives and fuzzy reasoning with respect to Chebyshev distance
7．1 Introduction
7．2 Robustness of fuzzy connectives with respect to Chebyshev distance
7．2．1 δ-equality and maximum perturbation of fuzzy sets
7．2．2 Robustness ofthree kinds of fuzzy connectives
7．3 Robustness of the generalized modus ponens based on Chebyshev distance
7．4 Discussions
Chapter 8 Robustness of fuzzy reasoning with respect to general divergence measures
8．1 Introduction
8．2 Constructions of DF-metrics and their properties
8．2．1 Definition of DF-metric
8．2．2 Constructions of DF-metrics
8．2．3 Properties of DF-metrics
8．3 Robustness of fuzzy connectives and fuzzy reasoning with respect to general divergence measures
8．3．1 Robustness of fuzzy connectives with respect to general divergence measures
8．3．2 Robustness of fuzzy reasoning with respect to general divergence measures
8．4 Discussions
Conclusions and Further Works
Acknowledgments
Bibliography
List of Publications and Research Projects
