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.

Comprehensive up-to-date account of results with applications of the results

Autorentext

Dr. John N Mordeson is a professor emeritus of Mathematics at Creighton University. He received his B.S., M.S., and Ph.D. from Iowa State University. He is a member of Phi Kappa Phi. He has published 20 books and over 200 journal articles. He is on the editorial board of numerous journals. He has served as an external examiner of Ph.D. candidates from India, South Africa, Bulgaria, and Pakistan. He has refereed for numerous journals and granting agencies. He is particularly interested in applying mathematics of uncertainty to combat the problem of human trafficking. Dr. Sunil Mathew is a faculty member in the Department of Mathematics, NIT Calicut, India. He has acquired his masters from St. Joseph's College Devagiri, Calicut, and Ph.D. from National Institute of Technology Calicut in the area of fuzzy graph theory. He has published more than 120 research papers and written 10 books. He is a member of several academic bodies and associations. He is an editor and reviewer of several international journals. He has an experience of 20 years in teaching and research. His current research topics include fuzzy graph theory, bio-computational modeling, graph theory, fractal geometry, and chaos. Ms. Gayathri G is currently pursuing research in the Department of Mathematics, National Institute of Technology Calicut, India. She took her master's degree in Mathematics from Government College Kasaragod, Kasaragod. She has got several publications in prestigious journals.

Inhalt
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.