Book description
Provides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets
This book examines fuzzy and intuitionistic fuzzy mathematics and unifies the latest existing works in literature. It enables readers to fully understand the mathematics of both fuzzy set and intuitionistic fuzzy set so that they can use either one in their applications.
Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh's extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measures; examines matrices and determinants of a fuzzy matrix; and teaches about fuzzy linear equations. Readers will also learn about fuzzy subgroups. The second to last chapter examines the application of fuzzy and intuitionistic fuzzy mathematics in image enhancement, segmentation, and retrieval. Finally, the book concludes with coverage the extension of fuzzy sets. This book:
 Covers both fuzzy and intuitionistic fuzzy sets and includes examples and practical applications
 Discusses intuitionistic fuzzy integrals and recent aggregation operators using Choquet integral, with examples
 Includes a chapter on applications in image processing using fuzzy and intuitionistic fuzzy sets
 Explains fuzzy matrix operations and features examples
Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set is an ideal text for graduate and research students, as well as professionals, in image processing, decisionmaking, pattern recognition, and control system design.
Table of contents
 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
 2.6 Operations on Fuzzy Numbers with Intervals
 2.7 Operations with Fuzzy Numbers based on α‐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

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
 7 Fuzzy Matrices and Determinants
 8 Fuzzy Subgroups
 9 Application of Fuzzy/Intuitionistic Fuzzy Set in Image Processing
 Chapter 10: Type‐2 Fuzzy Set
 Beyond Your Doubts
 Index
 End User License Agreement
Product information
 Title: Fuzzy Set and Its Extension
 Author(s):
 Release date: April 2019
 Publisher(s): Wiley
 ISBN: 9781119544197
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