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End User License Agreement
by Tamalika Chaira
Fuzzy Set and Its Extension
Cover
Preface
Organization of the Book
1 Fuzzy/Intuitionistic Fuzzy Set Theory
1.1 Introduction to Fuzzy Set
1.2 Mathematical Representation of Fuzzy Sets
1.3 Membership Function
1.4 Fuzzy Relations
1.5 Projection
1.6 Composition of Fuzzy Relation
1.7 Fuzzy Binary Relation
1.8 Transitive Closure of Fuzzy Binary Relation
1.9 Fuzzy Equivalence Relation
1.10 Intuitionistic Fuzzy Set
1.11 Construction of Intuitionistic Fuzzy Set
1.12 Intuitionistic Fuzzy Relations
1.13 Composition of Intuitionistic Fuzzy Relation
1.14 Intuitionistic Fuzzy Binary Relation
1.15 Summary
References
2 Playing with Fuzzy/Intuitionistic Fuzzy Numbers
2.1 Introduction
2.2 Fuzzy Numbers
2.3 Fuzzy Intervals
2.4 Zadeh’s Extension Principle
2.5 Fuzzy Numbers with α‐Levels‐Levels
2.6 Operations on Fuzzy Numbers with Intervals
2.7 Operations with Fuzzy Numbers based on α‐Levels‐Levels
2.8 Operations on Fuzzy Numbers Using Extension Principle
2.9 L–R Representation of Fuzzy Numbers
2.10 Intuitionistic Fuzzy Numbers
2.11 Triangular Intuitionistic Fuzzy Number
2.12 Operations Using Triangular Intuitionistic Fuzzy Numbers
2.13 Trapezoidal Intuitionistic Fuzzy Numbers
2.14 Cut Set of Intuitionistic Fuzzy Number
2.15 Distances Between Two Intuitionistic Fuzzy Numbers
2.16 Summary
References
3 Similarity Measures and Measures of Fuzziness
3.1 Introduction
3.2 Distance and Similarity Measures
3.3 Types of Distance Measure Between Fuzzy Sets
3.4 Types of Similarity Measures Between Fuzzy Sets
3.5 Generalized Fuzzy Number
3.6 Similarity Measures Between Two Fuzzy Numbers
3.7 Inclusion Measure
3.8 Measures of Fuzziness
3.9 Intuitionistic Fuzzy Distance and Similarity Measures
3.10 Intuitionistic Fuzzy Entropy
3.11 Different Types of Intuitionistic Fuzzy Entropies
3.12 Summary
References
4 Fuzzy/Intuitionistic Fuzzy Measures and Fuzzy Integrals
4.1 Introduction
4.2 Definition of Fuzzy Measure
4.3 Fuzzy Measures
4.4 Fuzzy Integrals
4.5 Intuitionistic Fuzzy Integral
4.6 Summary
References
5 Operations on Fuzzy/Intuitionistic Fuzzy Sets and Application in Decision Making
5.1 Introduction
5.2 Fuzzy Operations
5.3 Fuzzy Other Operators: Fuzzy T‐Norms and T‐Conorms
5.4 Implication Operator
5.5 Aggregation Operator with Application in Decision Making
5.6 Intuitionistic Fuzzy Operators
5.7 Intuitionistic Fuzzy Aggregation Operator
5.8 Example on Decision‐making Problems
5.9 Summary
References
6 Fuzzy Linear Equations
6.1 Introduction
6.2 Fuzzy Linear Equation
6.3 Solving Linear Equation Using Cramer's Rule
6.4 Inverse of a Fuzzy Matrix
6.5 Summary
References
7 Fuzzy Matrices and Determinants
7.1 Basic Matrix Theory
7.2 Fuzzy Matrices
7.3 Determinant of a Square Fuzzy Matrix
7.4 Adjoint of a Square Fuzzy Matrix
7.5 Properties of Reflexive Matrices
7.6 Generalized Inverse of a Fuzzy Matrix
7.7 Intuitionistic Fuzzy Matrix
7.8 Summary
References
8 Fuzzy Subgroups
8.1 Introduction
8.2 Theorems of Fuzzy Subgroup
8.3 Fuzzy‐level Subgroup
8.4 Fuzzy Normal Subgroup
8.5 Fuzzy Subgroups Using T‐norms
8.6 Product of Fuzzy Subgroups
8.7 Summary
References
9 Application of Fuzzy/Intuitionistic Fuzzy Set in Image Processing
9.1 Introduction
9.2 Digital Images
9.3 Image Enhancement
9.4 Thresholding
9.5 Edge Detection
9.6 Clustering
9.7 Mathematical Morphology
9.8 Summary
References
Chapter 10: Type‐2 Fuzzy Set
10.1 Introduction
10.2 Type‐2 Fuzzy Set
10.3 Operations on Type‐2 Fuzzy Set
10.4 Inclusion Measure and Similarity Measure
10.5 Interval Type‐2 Fuzzy Set
10.6 Application of Interval Type‐2 Fuzzy Set in Image Segmentation
10.7 Summary
References
Beyond Your Doubts
Index
End User License Agreement
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