ISBN: 3790814202
TITLE: Studies in Fuzziness and Soft Computing Vol. 20, 2nd Edition
AUTHOR: Mordeson
TOC:

FOREWORD V
PREFACE vii
ACKNOWLEDGMENTS ix
1 FUZZY SUBSETS 1
1.1 Fuzzy Relations 6
1.2 Operations on Fuzzy Relations 8
1.3 Reflexivity, Symmetry and Transitivity 11
1.4 Pattern Classification Based on Fuzzy Relations 12
1.5 Advanced Topics on Fuzzy Relations 16
1.6 References 20
2 FUZZY GRAPHS 21
2.1 Paths and Connectedness 22
2.2 Clusters 24
2.3 Cluster Analysis and Modeling of Information Networks 29
2.4 Connectivity in Fuzzy Graphs 32
2.5 Application to Cluster Analysis 39
2.6 Operations on Fuzzy Graphs 44
2.7 Fuzzy Intersection Equations 52
2.8 Fuzzy Graphs in Database Theory 58
2.9 References 61
3 FUZZY TOPOLOGICAL SPACES 67
3.1 Topological Spaces 67
3.2 Metric Spaces and Normed Linear Spaces 74
3.3 Fuzzy Topological Spaces 79
3.4 Sequences of Fuzzy Subsets 81
3.5 F-Continuous Functions 82
3.6 Compact Fuzzy Spaces 84
3.7 Iterated Fuzzy Subset Systems 85
3.8 Chaotic Iterations of Fuzzy Subsets 95
3.9 Starshaped Fuzzy Subsets 99
3.10 References 102
4 FUZZY DIGITAL TOPOLOGY 115
4.1 Introduction 115
4.2 Crisp Digital Topology 115
4.3 Fuzzy Connectedness 116
4.4 Fuzzy Components 118
4.5 Fuzzy Surroundedness 123
4.6 Components, Holes, and Surroundedness 124
4.7 Convexity 127
4.8 The Sup Projection 128
4.9 The Integral Projection 128
4.10 Fuzzy Digital Convexity 131
4.11 On Connectivity Properties of Grayscale Pictures 133
4.12 References 135
5 FUZZY GEOMETRY 137
5.1 Introduction 137
5.2 The Area and Perimeter of a Fuzzy Subset 137
5.3 The Height, Width and Diameter of a Fuzzy Subset 147
5.4 Distances Between Fuzzy Subsets 152
5.5 Fuzzy Rectangles 155
5.6 A Fuzzy Medial Axis Transformation Based on Fuzzy Disks 158
5.7 Fuzzy Triangles 163
5.8 Degree of Adjacency or Surroundedness 166
5.9 Image Enhancement and Thresholding Using Fuzzy Compactness 181
5.10 Fuzzy Plane Geometry: Points and Lines 189
5.11 Fuzzy Plane Geometry: Circles and Polygons 197
5.12 Fuzzy Plane Projective Geometry 204
5.13 A Modified Hausdorff Distance Between Fuzzy Subsets 207
5.14 References 214
6 FUZZY ABSTRACT ALGEBRA 219
6.1 Crisp Algebraic Structures 219
6.2 Fuzzy Substructures of Algebraic Structures 233
6.3 Fuzzy Submonoids and Automata Theory 238
6.4 Fuzzy Subgroups, Pattern Recognition and Coding Theory 240
6.5 Free Fuzzy Monoids and Coding Theory 245
6.6 Formal Power Series, Regular Fuzzy Languages, and Fuzzy Automata 252
6.7 Nonlinear Systems of Equations of Fuzzy Singletons 266
6.8 Localized Fuzzy Subrings 272
6.9 Local Examination of Fuzzy Intersection Equations 276
6.10 More on Coding Theory 281
6.11 Other Applications 286
6.12 References 287
LIST OF FIGURES 291
LIST OF TABLES 293
LIST OF SYMBOLS 295
INDEX 303
END
