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Fuzzy set and its extension : the intuitionistic fuzzy set / / Tamalika Chaira, Midnapore (West), West Bengal, India
| Fuzzy set and its extension : the intuitionistic fuzzy set / / Tamalika Chaira, Midnapore (West), West Bengal, India |
| Autore | Chaira Tamalika |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2019 |
| Descrizione fisica | 1 online resource (307 pages) |
| Disciplina | 511.3223 |
| Soggetto topico |
Fuzzy sets
Fuzzy numbers Set theory Approximation theory |
| ISBN |
1-119-54422-X
1-119-54420-3 1-119-54421-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface xiii -- Organization of the Book xv -- 1 Fuzzy/Intuitionistic Fuzzy Set Theory 1 -- 1.1 Introduction to Fuzzy Set 1 -- 1.2 Mathematical Representation of Fuzzy Sets 3 -- 1.3 Membership Function 6 -- 1.4 Fuzzy Relations 10 -- 1.5 Projection 13 -- 1.6 Composition of Fuzzy Relation 14 -- 1.7 Fuzzy Binary Relation 19 -- 1.8 Transitive Closure of Fuzzy Binary Relation 21 -- 1.9 Fuzzy Equivalence Relation 23 -- 1.10 Intuitionistic Fuzzy Set 24 -- 1.11 Construction of Intuitionistic Fuzzy Set 26 -- 1.12 Intuitionistic Fuzzy Relations 29 -- 1.13 Composition of Intuitionistic Fuzzy Relation 31 -- 1.13.1 Composition of IFR Using T-norms and T-conorms 32 -- 1.14 Intuitionistic Fuzzy Binary Relation 34 -- 1.14.1 Reflexive Property 34 -- 1.14.2 Symmetric Property 37 -- 1.14.3 Transitive Property 38 -- 1.15 Summary 39 -- References 39 -- 2 Playing with Fuzzy/Intuitionistic Fuzzy Numbers 41 -- 2.1 Introduction 41 -- 2.2 Fuzzy Numbers 41 -- 2.3 Fuzzy Intervals 42 -- 2.4 Zadeh́Ös Extension Principle 43 -- 2.4.1 Extension Principle for Two Variables 44 -- 2.5 Fuzzy Numbers with α-Levels 48 -- 2.6 Operations on Fuzzy Numbers with Intervals 52 -- 2.7 Operations with Fuzzy Numbers based on α-Levels 54 -- 2.8 Operations on Fuzzy Numbers Using Extension Principle 62 -- 2.8.1 Operations 63 -- 2.8.2 Examples on Operations of Fuzzy Numbers Using Extension Principle 64 -- 2.9 L-R Representation of Fuzzy Numbers 66 -- 2.10 Intuitionistic Fuzzy Numbers 73 -- 2.11 Triangular Intuitionistic Fuzzy Number 74 -- 2.12 Operations Using Triangular Intuitionistic Fuzzy Numbers 75 -- 2.13 Trapezoidal Intuitionistic Fuzzy Numbers 77 -- 2.14 Cut Set of Intuitionistic Fuzzy Number 78 -- 2.15 Distances Between Two Intuitionistic Fuzzy Numbers 80 -- 2.16 Summary 80 -- References 80 -- 3 Similarity Measures and Measures of Fuzziness 83 -- 3.1 Introduction 83 -- 3.2 Distance and Similarity Measures 83 -- 3.2.1 Distance Measure 84 -- 3.2.2 Similarity Measure 84 -- 3.3 Types of Distance Measure Between Fuzzy Sets 84.
3.4 Types of Similarity Measures Between Fuzzy Sets 85 -- 3.5 Generalized Fuzzy Number 85 -- 3.6 Similarity Measures Between Two Fuzzy Numbers 88 -- 3.7 Inclusion Measure 94 -- 3.8 Measures of Fuzziness 95 -- 3.8.1 Index of Fuzziness 95 -- 3.8.2 YageŕÖs Measure 96 -- 3.8.3 Fuzzy Entropy 96 -- 3.9 Intuitionistic Fuzzy Distance and Similarity Measures 98 -- 3.10 Intuitionistic Fuzzy Entropy 105 -- 3.11 Different Types of Intuitionistic Fuzzy Entropies 106 -- 3.12 Summary 107 -- References 107 -- 4 Fuzzy/Intuitionistic Fuzzy Measures and Fuzzy Integrals 111 -- 4.1 Introduction 111 -- 4.2 Definition of Fuzzy Measure 111 -- 4.3 Fuzzy Measures 112 -- 4.3.1 Sugeno Î"-Fuzzy Measure 112 -- 4.3.2 Belief Measure 115 -- 4.3.3 Plausibility Measure 116 -- 4.3.4 Possibility Measure and Necessity Measure 116 -- 4.3.4.1 Possibility Measure 117 -- 4.3.4.2 Necessity Measure 119 -- 4.4 Fuzzy Integrals 121 -- 4.4.1 Sugeno Integral 122 -- 4.4.2 Choquet Integral 125 -- 4.4.3 Sipos Integral 129 -- 4.5 Intuitionistic Fuzzy Integral 130 -- 4.5.1 Intuitionistic Fuzzy Choquet Integral 130 -- 4.6 Summary 131 -- References 131 -- 5 Operations on Fuzzy/Intuitionistic Fuzzy Sets and Application in Decision Making 133 -- 5.1 Introduction 133 -- 5.2 Fuzzy Operations 133 -- 5.2.1 Fuzzy Union 134 -- 5.2.2 Fuzzy Intersection 134 -- 5.2.3 Fuzzy Complements 134 -- 5.2.4 Algebraic Product 136 -- 5.2.5 Algebraic Sum 137 -- 5.2.6 Simple Difference 137 -- 5.2.7 Bounded Sum 137 -- 5.2.8 Bounded Difference 137 -- 5.2.9 Bounded Product 137 -- 5.3 Fuzzy Other Operators: Fuzzy T-Norms and T-Conorms 138 -- 5.3.1 Definition of T-Norm 138 -- 5.3.2 Definition of T-Conorm 139 -- 5.4 Implication Operator 142 -- 5.5 Aggregation Operator with Application in Decision Making 144 -- 5.5.1 Fuzzy Weighted Averaging Operator (FWA) 144 -- 5.5.2 Fuzzy Ordered Weighted Averaging Operator (FOWA) 145 -- 5.5.3 Fuzzy Generalized Ordered Weighted Averaging Operator (GOWA) 146 -- 5.5.4 Fuzzy Hybrid Averaging Operator (FHA) 146 -- 5.5.5 Fuzzy Quasi-Arithmetic Weighted Averaging Operator 146. 5.5.6 Induced Generalized Fuzzy Averaging Operator (IGOWA) 147 -- 5.5.7 Choquet Aggregation Operator 149 -- 5.5.8 Induced Choquet Ordered Aggregation Operator 150 -- 5.6 Intuitionistic Fuzzy Operators 152 -- 5.7 Intuitionistic Fuzzy Aggregation Operator 153 -- 5.7.1 Generalized Intuitionistic Fuzzy Aggregation Operator 153 -- 5.7.2 Generalized Intuitionistic Fuzzy Ordered Weighting Operator (GIFOWA) 155 -- 5.7.3 Generalized Intuitionistic Fuzzy Hybrid Operator 157 -- 5.7.4 Intuitionistic Fuzzy Weighted Geometric Operator (IFWG) 160 -- 5.7.5 Intuitionistic Fuzzy Ordered Weighted Geometric Operator 161 -- 5.7.6 Induced Generalized Intuitionistic Fuzzy Ordered Averaging Operator 161 -- 5.7.7 Intuitionistic Fuzzy Choquet Integral Operator 162 -- 5.7.8 Induced Intuitionistic Fuzzy Choquet Integral Operator 162 -- 5.8 Example on Decision-making Problems 164 -- 5.9 Summary 168 -- References 168 -- 6 Fuzzy Linear Equations 171 -- 6.1 Introduction 171 -- 6.2 Fuzzy Linear Equation 172 -- 6.2.1 Problem of Finding an Unknown Number 173 -- 6.3 Solving Linear Equation Using CrameŕÖs Rule 177 -- 6.4 Inverse of a Fuzzy Matrix 182 -- 6.5 Summary 189 -- References 189 -- 7 Fuzzy Matrices and Determinants 191 -- 7.1 Basic Matrix Theory 191 -- 7.1.1 Matrix Addition 192 -- 7.1.2 Matrix Multiplication 193 -- 7.1.3 Transpose of a Matrix 193 -- 7.2 Fuzzy Matrices 194 -- 7.2.1 Matrix Addition, Multiplication, Max, Min Operations 197 -- 7.2.2 Identity Matrix 202 -- 7.3 Determinant of a Square Fuzzy Matrix 202 -- 7.3.1 Examples of Fuzzy Determinants 203 -- 7.4 Adjoint of a Square Fuzzy Matrix 206 -- 7.4.1 Few Proposition of Adjoint of Fuzzy Matrices 207 -- 7.5 Properties of Reflexive Matrices 212 -- 7.6 Generalized Inverse of a Fuzzy Matrix 215 -- 7.7 Intuitionistic Fuzzy Matrix 216 -- 7.7.1 Identity Matrix 217 -- 7.7.2 Null Matrix 218 -- 7.7.3 Generalized Inverse of Intuitionistic Fuzzy Matrix 218 -- 7.8 Summary 218 -- References 218 -- 8 Fuzzy Subgroups 221 -- 8.1 Introduction 221 -- 8.2 Theorems of Fuzzy Subgroup 222. 8.3 Fuzzy-level Subgroup 226 -- 8.4 Fuzzy Normal Subgroup 228 -- 8.5 Fuzzy Subgroups Using T-norms 229 -- 8.6 Product of Fuzzy Subgroups 231 -- 8.7 Summary 234 -- References 235 -- 9 Application of Fuzzy/Intuitionistic Fuzzy Set in Image Processing 237 -- 9.1 Introduction 237 -- 9.2 Digital Images 237 -- 9.3 Image Enhancement 238 -- 9.3.1 Fuzzy Enhancement Method 238 -- 9.3.2 Intuitionistic Fuzzy Enhancement Method 239 -- 9.4 Thresholding 240 -- 9.4.1 Intuitionistic Fuzzy Thresholding Method 242 -- 9.4.2 Fuzzy Thresholding Method 244 -- 9.5 Edge Detection 244 -- 9.5.1 Fuzzy Edge-detection Method 245 -- 9.5.2 Intuitionistic Fuzzy Edge Detection 246 -- 9.6 Clustering 248 -- 9.6.1 Fuzzy c Means Clustering (FCM) 248 -- 9.6.2 Intuitionistic Fuzzy Clustering 249 -- 9.6.3 Kernel Clustering 250 -- 9.7 Mathematical Morphology 252 -- 9.7.1 Fuzzy Approach 254 -- 9.7.2 Intuitionistic Fuzzy Approach 254 -- 9.8 Summary 256 -- References 256 -- 10 Type-2 Fuzzy Set 259 -- 10.1 Introduction 259 -- 10.2 Type-2 Fuzzy Set 260 -- 10.3 Operations on Type-2 Fuzzy Set 263 -- 10.4 Inclusion Measure and Similarity Measure 267 -- 10.4.1 Similarity Measure 268 -- 10.5 Interval Type-2 Fuzzy Set 270 -- 10.6 Application of Interval Type-2 Fuzzy Set in Image Segmentation 271 -- 10.7 Summary 273 -- References 273 -- Beyond Your Doubts 275 -- Index 281. |
| Record Nr. | UNINA-9910555146303321 |
Chaira Tamalika
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fuzzy set and its extension : the intuitionistic fuzzy set / / Tamalika Chaira, Midnapore (West), West Bengal, India
| Fuzzy set and its extension : the intuitionistic fuzzy set / / Tamalika Chaira, Midnapore (West), West Bengal, India |
| Autore | Chaira Tamalika |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2019 |
| Descrizione fisica | 1 online resource (307 pages) |
| Disciplina | 511.3223 |
| Soggetto topico |
Fuzzy sets
Fuzzy numbers Set theory Approximation theory |
| ISBN |
1-119-54422-X
1-119-54420-3 1-119-54421-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface xiii -- Organization of the Book xv -- 1 Fuzzy/Intuitionistic Fuzzy Set Theory 1 -- 1.1 Introduction to Fuzzy Set 1 -- 1.2 Mathematical Representation of Fuzzy Sets 3 -- 1.3 Membership Function 6 -- 1.4 Fuzzy Relations 10 -- 1.5 Projection 13 -- 1.6 Composition of Fuzzy Relation 14 -- 1.7 Fuzzy Binary Relation 19 -- 1.8 Transitive Closure of Fuzzy Binary Relation 21 -- 1.9 Fuzzy Equivalence Relation 23 -- 1.10 Intuitionistic Fuzzy Set 24 -- 1.11 Construction of Intuitionistic Fuzzy Set 26 -- 1.12 Intuitionistic Fuzzy Relations 29 -- 1.13 Composition of Intuitionistic Fuzzy Relation 31 -- 1.13.1 Composition of IFR Using T-norms and T-conorms 32 -- 1.14 Intuitionistic Fuzzy Binary Relation 34 -- 1.14.1 Reflexive Property 34 -- 1.14.2 Symmetric Property 37 -- 1.14.3 Transitive Property 38 -- 1.15 Summary 39 -- References 39 -- 2 Playing with Fuzzy/Intuitionistic Fuzzy Numbers 41 -- 2.1 Introduction 41 -- 2.2 Fuzzy Numbers 41 -- 2.3 Fuzzy Intervals 42 -- 2.4 Zadeh́Ös Extension Principle 43 -- 2.4.1 Extension Principle for Two Variables 44 -- 2.5 Fuzzy Numbers with α-Levels 48 -- 2.6 Operations on Fuzzy Numbers with Intervals 52 -- 2.7 Operations with Fuzzy Numbers based on α-Levels 54 -- 2.8 Operations on Fuzzy Numbers Using Extension Principle 62 -- 2.8.1 Operations 63 -- 2.8.2 Examples on Operations of Fuzzy Numbers Using Extension Principle 64 -- 2.9 L-R Representation of Fuzzy Numbers 66 -- 2.10 Intuitionistic Fuzzy Numbers 73 -- 2.11 Triangular Intuitionistic Fuzzy Number 74 -- 2.12 Operations Using Triangular Intuitionistic Fuzzy Numbers 75 -- 2.13 Trapezoidal Intuitionistic Fuzzy Numbers 77 -- 2.14 Cut Set of Intuitionistic Fuzzy Number 78 -- 2.15 Distances Between Two Intuitionistic Fuzzy Numbers 80 -- 2.16 Summary 80 -- References 80 -- 3 Similarity Measures and Measures of Fuzziness 83 -- 3.1 Introduction 83 -- 3.2 Distance and Similarity Measures 83 -- 3.2.1 Distance Measure 84 -- 3.2.2 Similarity Measure 84 -- 3.3 Types of Distance Measure Between Fuzzy Sets 84.
3.4 Types of Similarity Measures Between Fuzzy Sets 85 -- 3.5 Generalized Fuzzy Number 85 -- 3.6 Similarity Measures Between Two Fuzzy Numbers 88 -- 3.7 Inclusion Measure 94 -- 3.8 Measures of Fuzziness 95 -- 3.8.1 Index of Fuzziness 95 -- 3.8.2 YageŕÖs Measure 96 -- 3.8.3 Fuzzy Entropy 96 -- 3.9 Intuitionistic Fuzzy Distance and Similarity Measures 98 -- 3.10 Intuitionistic Fuzzy Entropy 105 -- 3.11 Different Types of Intuitionistic Fuzzy Entropies 106 -- 3.12 Summary 107 -- References 107 -- 4 Fuzzy/Intuitionistic Fuzzy Measures and Fuzzy Integrals 111 -- 4.1 Introduction 111 -- 4.2 Definition of Fuzzy Measure 111 -- 4.3 Fuzzy Measures 112 -- 4.3.1 Sugeno Î"-Fuzzy Measure 112 -- 4.3.2 Belief Measure 115 -- 4.3.3 Plausibility Measure 116 -- 4.3.4 Possibility Measure and Necessity Measure 116 -- 4.3.4.1 Possibility Measure 117 -- 4.3.4.2 Necessity Measure 119 -- 4.4 Fuzzy Integrals 121 -- 4.4.1 Sugeno Integral 122 -- 4.4.2 Choquet Integral 125 -- 4.4.3 Sipos Integral 129 -- 4.5 Intuitionistic Fuzzy Integral 130 -- 4.5.1 Intuitionistic Fuzzy Choquet Integral 130 -- 4.6 Summary 131 -- References 131 -- 5 Operations on Fuzzy/Intuitionistic Fuzzy Sets and Application in Decision Making 133 -- 5.1 Introduction 133 -- 5.2 Fuzzy Operations 133 -- 5.2.1 Fuzzy Union 134 -- 5.2.2 Fuzzy Intersection 134 -- 5.2.3 Fuzzy Complements 134 -- 5.2.4 Algebraic Product 136 -- 5.2.5 Algebraic Sum 137 -- 5.2.6 Simple Difference 137 -- 5.2.7 Bounded Sum 137 -- 5.2.8 Bounded Difference 137 -- 5.2.9 Bounded Product 137 -- 5.3 Fuzzy Other Operators: Fuzzy T-Norms and T-Conorms 138 -- 5.3.1 Definition of T-Norm 138 -- 5.3.2 Definition of T-Conorm 139 -- 5.4 Implication Operator 142 -- 5.5 Aggregation Operator with Application in Decision Making 144 -- 5.5.1 Fuzzy Weighted Averaging Operator (FWA) 144 -- 5.5.2 Fuzzy Ordered Weighted Averaging Operator (FOWA) 145 -- 5.5.3 Fuzzy Generalized Ordered Weighted Averaging Operator (GOWA) 146 -- 5.5.4 Fuzzy Hybrid Averaging Operator (FHA) 146 -- 5.5.5 Fuzzy Quasi-Arithmetic Weighted Averaging Operator 146. 5.5.6 Induced Generalized Fuzzy Averaging Operator (IGOWA) 147 -- 5.5.7 Choquet Aggregation Operator 149 -- 5.5.8 Induced Choquet Ordered Aggregation Operator 150 -- 5.6 Intuitionistic Fuzzy Operators 152 -- 5.7 Intuitionistic Fuzzy Aggregation Operator 153 -- 5.7.1 Generalized Intuitionistic Fuzzy Aggregation Operator 153 -- 5.7.2 Generalized Intuitionistic Fuzzy Ordered Weighting Operator (GIFOWA) 155 -- 5.7.3 Generalized Intuitionistic Fuzzy Hybrid Operator 157 -- 5.7.4 Intuitionistic Fuzzy Weighted Geometric Operator (IFWG) 160 -- 5.7.5 Intuitionistic Fuzzy Ordered Weighted Geometric Operator 161 -- 5.7.6 Induced Generalized Intuitionistic Fuzzy Ordered Averaging Operator 161 -- 5.7.7 Intuitionistic Fuzzy Choquet Integral Operator 162 -- 5.7.8 Induced Intuitionistic Fuzzy Choquet Integral Operator 162 -- 5.8 Example on Decision-making Problems 164 -- 5.9 Summary 168 -- References 168 -- 6 Fuzzy Linear Equations 171 -- 6.1 Introduction 171 -- 6.2 Fuzzy Linear Equation 172 -- 6.2.1 Problem of Finding an Unknown Number 173 -- 6.3 Solving Linear Equation Using CrameŕÖs Rule 177 -- 6.4 Inverse of a Fuzzy Matrix 182 -- 6.5 Summary 189 -- References 189 -- 7 Fuzzy Matrices and Determinants 191 -- 7.1 Basic Matrix Theory 191 -- 7.1.1 Matrix Addition 192 -- 7.1.2 Matrix Multiplication 193 -- 7.1.3 Transpose of a Matrix 193 -- 7.2 Fuzzy Matrices 194 -- 7.2.1 Matrix Addition, Multiplication, Max, Min Operations 197 -- 7.2.2 Identity Matrix 202 -- 7.3 Determinant of a Square Fuzzy Matrix 202 -- 7.3.1 Examples of Fuzzy Determinants 203 -- 7.4 Adjoint of a Square Fuzzy Matrix 206 -- 7.4.1 Few Proposition of Adjoint of Fuzzy Matrices 207 -- 7.5 Properties of Reflexive Matrices 212 -- 7.6 Generalized Inverse of a Fuzzy Matrix 215 -- 7.7 Intuitionistic Fuzzy Matrix 216 -- 7.7.1 Identity Matrix 217 -- 7.7.2 Null Matrix 218 -- 7.7.3 Generalized Inverse of Intuitionistic Fuzzy Matrix 218 -- 7.8 Summary 218 -- References 218 -- 8 Fuzzy Subgroups 221 -- 8.1 Introduction 221 -- 8.2 Theorems of Fuzzy Subgroup 222. 8.3 Fuzzy-level Subgroup 226 -- 8.4 Fuzzy Normal Subgroup 228 -- 8.5 Fuzzy Subgroups Using T-norms 229 -- 8.6 Product of Fuzzy Subgroups 231 -- 8.7 Summary 234 -- References 235 -- 9 Application of Fuzzy/Intuitionistic Fuzzy Set in Image Processing 237 -- 9.1 Introduction 237 -- 9.2 Digital Images 237 -- 9.3 Image Enhancement 238 -- 9.3.1 Fuzzy Enhancement Method 238 -- 9.3.2 Intuitionistic Fuzzy Enhancement Method 239 -- 9.4 Thresholding 240 -- 9.4.1 Intuitionistic Fuzzy Thresholding Method 242 -- 9.4.2 Fuzzy Thresholding Method 244 -- 9.5 Edge Detection 244 -- 9.5.1 Fuzzy Edge-detection Method 245 -- 9.5.2 Intuitionistic Fuzzy Edge Detection 246 -- 9.6 Clustering 248 -- 9.6.1 Fuzzy c Means Clustering (FCM) 248 -- 9.6.2 Intuitionistic Fuzzy Clustering 249 -- 9.6.3 Kernel Clustering 250 -- 9.7 Mathematical Morphology 252 -- 9.7.1 Fuzzy Approach 254 -- 9.7.2 Intuitionistic Fuzzy Approach 254 -- 9.8 Summary 256 -- References 256 -- 10 Type-2 Fuzzy Set 259 -- 10.1 Introduction 259 -- 10.2 Type-2 Fuzzy Set 260 -- 10.3 Operations on Type-2 Fuzzy Set 263 -- 10.4 Inclusion Measure and Similarity Measure 267 -- 10.4.1 Similarity Measure 268 -- 10.5 Interval Type-2 Fuzzy Set 270 -- 10.6 Application of Interval Type-2 Fuzzy Set in Image Segmentation 271 -- 10.7 Summary 273 -- References 273 -- Beyond Your Doubts 275 -- Index 281. |
| Record Nr. | UNINA-9910829839903321 |
|
Chaira Tamalika
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||