The book deals with fuzzy graph theory, fuzzy topology, fuzzy geometry, and fuzzy abstract algebra. The purpose of the book is to present the concepts of fuzzy mathematics which have applications to engineering, computer science, and mathematics. Some specific application areas are cluster analysis, digital image processing, fractal compression, chaotic fuzzy mappings, coding theory, automata theory, and nonlinear systems of fuzzy equations. The book is written with engineers and computer scientists in mind. Some mathematical sophistication is required of the reader. However the style is geared to a general audience. Most theorems are stated without proof and many examples are presented. Crisp results of mathematics are reviewed as needed.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
20
9 s/w Tabellen, 20 s/w Abbildungen
20 figures, 9 tables, references
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Gewicht
ISBN-13
978-3-7908-1121-6 (9783790811216)
Schweitzer Klassifikation
Fuzzy Subsets: Fuzzy Relations; Operations on Fuzzy Relations; Reflexivity, Symmetry and Transitivity; Pattern Classfication Based on Fuzzy Relations; Advanced Topics on Fuzzy Relations; References.- Fuzzy Graphs: Paths and Connectedness; Clusters; Cluster Analysis and Modeling of Information Networks; Connectivity in Fuzzy Graphs; Application to Cluster Analysis; Operations on Fuzzy Graphs; Fuzzy Intersection Equations; Fuzzy Graphs in Database Theory; References.- Fuzzy Topological Spaces: Topological Spaces; Metric Spaces and Normed Linear Spaces; Fuzzy Topological Spaces; Sequences of Fuzzy Subsets; F-Continuous Functions; Compact Fuzzy Spaces; Iterated Fuzzy Subset Systems; Chaotic Iterations of Fuzzy Subsets; Starshaped Fuzzy Subsets; References.- Fuzzy Digital Topology: Introduction; Crisp Digital Topology; Fuzzy Connectedness; Fuzzy Components; Fuzzy Surroundedness; Components, Holes, and Surroundedness; Convexity; The Sup Projection; The Integral Projection; Fuzzy Digital Convexity; On Connectivity Properties of Grayscale Pictures; References.- Fuzzy Geometry: Introduction; The Area and Perimeter of a Fuzzy Subset; The Height, Width and Diameter of a Fuzzy Subset; Distances between Fuzzy Subsets; Fuzzy Rectangles; A Fuzzy Medial Axis Transformation Based on Fuzzy Disks; Fuzzy Triangles; Fuzzy Plane Geometry: Points and Lines; Fuzzy Plane Projective Geometry; References.- Fuzzy Abstract Algebra: Crisp Algebraic Structures; Fuzzy Substructures of Algebraic Structures; Fuzzy Submonoids and Automata Theory; Fuzzy Subgroups, Pattern Recognition and Coding Theory; Free Fuzzy Monoids and Coding Theory; Formal Power Series, Regular Fuzzy Languages, and Fuzzy Automata; Nonlinear Systems of Equations of Fuzzy Singletons; More on Coding Theory; Other Applications; References.
