Fuzzy Mathematics An Introduction for Engineers and Scientists /

• Κύριοι συγγραφείς: Mordeson, John N. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Nair, Premchand S. (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Heidelberg : Physica-Verlag HD : Imprint: Physica, 2001.
• Έκδοση: 2nd ed. 2001.
• Σειρά: Studies in Fuzziness and Soft Computing, 20
• Θέματα: Mathematical logic.; Computer science-Mathematics.; Mathematics.; Computational intelligence.; Economic theory.; Mathematical Logic and Foundations.; Mathematics of Computing.; Mathematics, general.; Math Applications in Computer Science.; Computational Intelligence.; Economic Theory/Quantitative Economics/Mathematical Methods.

In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had sugge...

Πίνακας περιεχομένων:

• 1 Fuzzy Subsets
• 1.1 Fuzzy Relations
• 1.2 Operations on Fuzzy Relations
• 1.3 Reflexivity, Symmetry and Transitivity
• 1.4 Pattern Classification Based on Fuzzy Relations
• 1.5 Advanced Topics on Fuzzy Relations
• 1.6 References
• 2 Fuzzy Graphs
• 2.1 Paths and Connectedness
• 2.2 Clusters
• 2.3 Cluster Analysis and Modeling of Information Networks
• 2.4 Connectivity in Fuzzy Graphs
• 2.5 Application to Cluster Analysis
• 2.6 Operations on Fuzzy Graphs
• 2.7 Fuzzy Intersection Equations
• 2.8 Fuzzy Graphs in Database Theory
• 2.9 References
• 3 Fuzzy Topological Spaces
• 3.1 Topological Spaces
• 3.2 Metric Spaces and Normed Linear Spaces
• 3.3 Fuzzy Topological Spaces
• 3.4 Sequences of Fuzzy Subsets
• 3.5 F-Continuous Functions
• 3.6 Compact Fuzzy Spaces
• 3.7 Iterated Fuzzy Subset Systems
• 3.8 Chaotic Iterations of Fuzzy Subsets
• 3.9 Starshaped Fuzzy Subsets
• 3.10 References
• 4 Fuzzy Digital Topology
• 4.1 Introduction
• 4.2 Crisp Digital Topology
• 4.3 Fuzzy Connectedness
• 4.4 Fuzzy Components
• 4.5 Fuzzy Surroundedness
• 4.6 Components, Holes, and Surroundedness
• 4.7 Convexity
• 4.8 The Sup Projection
• 4.9 The Integral Projection
• 4.10 Fuzzy Digital Convexity
• 4.11 On Connectivity Properties of Grayscale Pictures
• 4.12 References
• 5 Fuzzy Geometry
• 5.1 Introduction
• 5.2 The Area and Perimeter of a Fuzzy Subset
• 5.3 The Height, Width and Diameter of a Fuzzy Subset
• 5.4 Distances Between Fuzzy Subsets
• 5.5 Fuzzy Rectangles
• 5.6 A Fuzzy Medial Axis Transformation Based on Fuzzy Disks
• 5.7 Fuzzy Triangles
• 5.8 Degree of Adjacency or Surroundedness
• 5.9 Image Enhancement and Thresholding Using Fuzzy Compactness
• 5.10 Fuzzy Plane Geometry: Points and Lines
• 5.11 Fuzzy Plane Geometry: Circles and Polygons
• 5.12 Fuzzy Plane Projective Geometry
• 5.13 A Modified Hausdorff Distance Between Fuzzy Subsets.
• 5.14 References
• 6 Fuzzy Abstract Algebra
• 6.1 Crisp Algebraic Structures
• 6.2 Fuzzy Substructures of Algebraic Structures
• 6.3 Fuzzy Submonoids and Automata Theory
• 6.4 Fuzzy Subgroups, Pattern Recognition and Coding Theory
• 6.5 Free Fuzzy Monoids and Coding Theory
• 6.6 Formal Power Series, Regular Fuzzy Languages, and Fuzzy Automata
• 6.7 Nonlinear Systems of Equations of Fuzzy Singletons
• 6.8 Localized Fuzzy Subrings
• 6.9 Local Examination of Fuzzy Intersection Equations
• 6.10 More on Coding Theory
• 6.11 Other Applications
• 6.12 References
• List of Figures
• List of Tables
• List of Symbols.