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 Lotfi A.Zadeh's theory of perception, while the concept of nonlinear approx­ imation is the driving force behind the success of the consumer electronics products manufacturing. It is fair to say fuzzy graph theory paved the way for engineers to build many rule-based expert systems. In the open literature, there are many papers written on the subject of fuzzy graph theory. However, there are relatively books available on the very same topic. Professors' Mordeson and Nair have made a real contribution in putting together a very com­ prehensive book on fuzzy graphs and fuzzy hypergraphs. In particular, the discussion on hypergraphs certainly is an innovative idea. For an experienced engineer who has spent a great deal of time in the lab­ oratory, it is usually a good idea to revisit the theory. Professors Mordeson and Nair have created such a volume which enables engineers and design­ ers to benefit from referencing in one place. In addition, this volume is a testament to the numerous contributions Professor John N. Mordeson and his associates have made to the mathematical studies in so many different topics of fuzzy mathematics. 

 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.