Fuzzy Graphs and Fuzzy Hypergraphs

• Main Authors: Mordeson, John N. (Author, http://id.loc.gov/vocabulary/relators/aut), Nair, Premchand S. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Heidelberg : Physica-Verlag HD : Imprint: Physica, 2000.
• Edition: 1st ed. 2000.
• Series: Studies in Fuzziness and Soft Computing, 46
• Subjects: Discrete mathematics.; Artificial intelligence.; Data structures (Computer science).; Combinatorics.; Computer science-Mathematics.; Information technology.; Business-Data processing.; Discrete Mathematics.; Artificial Intelligence.; Data Structures and Information Theory.; Mathematics of Computing.; IT in Business.

In the course of fuzzy technological development, fuzzy graph theory was identified quite early on for its importance in making things work. Two very important and useful concepts are those of granularity and of nonlinear ap­ proximations. The concept of granularity has evolved as a cornerstone of L...

Table of Contents:

• 1 Fuzzy Subsets
• 1.1 Fuzzy Relations
• 1.2 Fuzzy Equivalence Relations
• 1.3 Pattern Classification
• 1.4 Similarity Relations
• 1.5 References
• 2 Fuzzy Graphs
• 2.1 Paths and Connectedness
• 2.2 Fuzzy Line Graphs
• 2.3 Fuzzy Interval Graphs
• 2.4 Operations on Fuzzy Graphs
• 2.5 On Fuzzy Tree Definition
• 2.6 References
• 3 Applications of Fuzzy Graphs
• 3.1 Clusters
• 3.2 Cluster Analysis
• 3.3 Application to Cluster Analysis
• 3.4 Fuzzy Intersection Equations
• 3.5 Fuzzy Graphs in Database Theory
• 3.6 A Description of Strengthening and Weakening Members of a Group
• 3.7 An Application to the Problem Concerning Group Structure
• 3.8 References
• 4 Fuzzy Hypergraphs
• 4.1 Fuzzy Hypergraphs
• 4.2 Fuzzy Transversals of Fuzzy Hypergraphs
• 4.3 Coloring of Fuzzy Hypergraphs
• 4.4 Intersecting Fuzzy Hypergraphs
• 4.5 Hebbian Structures
• 4.6 Additional Applications
• 4.7 References
• List of Figures
• List of Tables
• List of Symbols.