Fuzzy Set and Its Extension : The Intuitionistic Fuzzy Set /: The Intuitionistic Fuzzy Set. (2019)

• Record Type: Book
• Further Information: Note: Tamalika Chaira.
• Authors: Chaira, Tamalika
• Contents: Organization of the book Preface Chapter 1: Fuzzy/intuitionistic fuzzy set theory 1.1 Introduction to fuzzy set 1.2 Mathematical representation of fuzzy set 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 (IFR) 1.13 Composition of intuitionistic fuzzy relation 1.13.1 Composition of IFR using t norms and co norms 1.14 Intuitionistic fuzzy binary relation 1.15 Summary 1.16 References Chapter 2: 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- intervals 2.6 Operation on fuzzy numbers with intervals 2.7 Operation on fuzzy numbers based on α- level 2.8 Operations on fuzzy numbers using extension principle 2.8.1 Examples on arithmetic operation on fuzzy numbers using extension principle 2.9 L-R representation of fuzzy numbers 2.10 Intuitionistic fuzzy number 2.11 Triangular intuitionistic fuzzy numbers 2.12 Operations using triangular intuitionistic fuzzy numbers 2.13 Trapezoidal intuitionistic fuzzy number 2.14 Cut set of triangular fuzzy number 2.15 Distance between two intuitionistic fuzzy number 2.16 Summary 2.17 References Chapter 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 using fuzzy numbers 3.7 Inclusion measure 3.8 Measures of fuzziness 3.8.1 Index of fuzziness 3.8.2 Yager’s measure 3.8.3 Entropy 3.9 Intuitionistic fuzzy distance measures 3.10 Intuitionistic fuzzy entropy 3.11 Different types of entropies 3.12 Summary References Chapter 4: Fuzzy/Intuitionistic fuzzy measures and fuzzy integrals 4.1 Introduction 4.2 Definition of Fuzzy measure 4.3 Fuzzy measures 4.3.1 Sugeno λ- measure 4.3.2 Belief measure 4.3.3 Plausibility measure 4.3.4 Possibility and necessity measures Fuzzy integrals; ; 4.4 Fuzzy integral 4.4.1 Sugeno integral 4.4.2 Choquet integral 4.4.3 Sipos Integral 4.5 Intuitionistic fuzzy Choquet integral 4.6 Summary References Chapter 5: Operations on fuzzy/intuitionistic fuzzy sets and application in decision making 5.1 Introduction 5.2 Fuzzy operation 5.3 Fuzzy other operators - t norms and t-conorms 5.4 Implication operator 5.5 Fuzzy aggregation operator with application in decision making a) Fuzzy weighted averaging operator b) Fuzzy ordered weighted averaging operator c) Fuzzy generalized ordered weighted averaging operator (GOWA) d) Fuzzy hybrid averaging operator(FHA) e) Fuzzy quasi arithmetic weighted averaging operator f) Induced fuzzy generalized averaging operator g) Choquet aggregation operator h) Induced Choquet ordered aggregation operator 5.6 Intuitionistic fuzzy operator 5.7 Intuitionistic fuzzy aggregation operator a) Generalized intuitionistic fuzzy aggregation operator b) Generalized intuitionistic fuzzy ordered weighting operator c) Generalized intuitionistic fuzzy hybrid operator(FHA) d) Intuitionistic fuzzy weighted geometric operator e) Intuitionistic fuzzy ordered weighted geometric operator f) Induced generalized intuitionistic fuzzy ordered averaging operator g) Intuitionistic fuzzy Choquet integral operator h) Induced intuitionistic fuzzy Choquet integral operator 5.8 Example on decision making problem 5.9 Summary References Chapter 6: Fuzzy linear equation 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 Chapter 7: Fuzzy matrices and determinants 7.1 Basic matrix theory 7.2 Fuzzy matrices 7.3 Determinant of a square fuzzy matrix 7.3.1 Examples of fuzzy determinants 7.4 Adjoint of a square fuzzy matrix 7.4.1 Few proposition of adjoint fuzzy matrices 7.5 Reflexive fuzzy matrix 7.6 Generalized inverse of a fuzzy matrix 7.7 Intuitionistic fuzzy matrix 7.8 Summary References Chapter 8: Fuzzy subgroups 8.1 Introduction 8.2 Properties of fuzzy subgroups 8.3 Fuzzy level sub group 8.4 Fuzzy normal subgroup 8.5 Fuzzy subgroups using t-norms 8.6 Product of fuzzy subgroup 8.7 Summary References Chapter 9: Application of Fuzzy/Intuitionistic fuzzy set in image processing 9.1 Introduction 9.2 Digital images 9.3 Image enhancement 9.3.1 Fuzzy enhancement method 9.3.2 Intuitionistic fuzzy enhancement method 9.4 Image thresholding 9.4.1 Intuitionistic fuzzy thresholding method 9.4.2 Fuzzy thresholding method 9.5 Image edge detection 9.5.1 Fuzzy edge detection 9.5.2 Intuitionistic fuzzy detection 9.6 Clustering 9.6.1 Fuzzy c means clustering 9.6.2 Intuitionistic fuzzy clustering 9.6.3 Kernel clustering 9.7 Mathematical morphology 9.7.1 Fuzzy method 9.7.2 Intuitionistic fuzzy method 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 processing 10.7 Summary References Problems
• Edition: 1st
• Publisher Details: Wiley
• Publication Date: 2019
• Extent: 1 online resource (304 pages)
• Languages: English
• ISBNs: 9781119544227
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.