The book 5 by mordeson and nair entitled fuzzy graphs and fuzzy hypergraphs is an excellent source for research in fuzzy graphs and fuzzy hypergraphs. Category of p om lfuzzy graphs and hypergraphs 53 it is obvious that. In this paper we are giving an overview on the fuzzy graph and its various kinds. May 19, 2000 professors mordeson and nair have made a real contribution in putting together a very com prehensive book on fuzzy graphs and fuzzy hypergraphs. In section 4, we discuss how the concept of qrung orthopair fuzzy directed hypergraphs can be applied to analyze the real life problems. Bhattacharya gave some remarks on fuzzy graphs in 5.
Bhutani and rosenfeld introduced the concept of mstrong fuzzy graphs in 7 and studied. A fuzzy subgraph h of g is defined by a fuzzy subset. Nair, fuzzy graphs and fuzzy hypergraphs physica verlag, heidelberg 1998. Also it is proved that the effective edge coloring of a fuzzy graph g is not. This function is also called a membership function. Certain concepts of bipolar fuzzy directed hypergraphs. In the course of fuzzy technological development, fuzzy graph theory was identified quite. Pal 2012, bipolar fuzzy hypergraphs, international. Also we investigate relations between operations union, join, and complement on bipolar fuzzy graphs. Operations on intuitionistic fuzzy graph structures sciencedirect. Some results on point set domination of fuzzy graphs in.
A description of strengthening and weakening members of a group 3. Malarvizhi discussed the isomorphism between fuzzy graphs and some properties of. Kaufmann 7 presented the idea of fuzzy hypergraphs. Fuzzy set theoryand its applications, fourth edition. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Rosenfeld 11 discussed the concept of fuzzy graphs whose basic idea was introduced by kauffmann 8. In this paper, the novel concept of dombi fuzzy graph is introduced. A dominating set d of a fuzzy graph is said to be a point set dominating set of a fuzzy graph if for every s.
Nair, fuzzy graphs and fuzzy hypergraphs, physica verlag publication, heidelbserg, second edition 2001. The elements of v are thought of as vertices of the graph and the elements of r are thought of as the edges similarly, any fuzzy relation. An application to the problem concerning group structure connectedness of a fuzzy graph 4. Operations on fuzzy hypergraphs were introduced by berge 3. Vague fuzzy incidence graphs, new mathematics and natural computation 14 2 2018 203219. Professors mordeson and nair have made a real contribution in putting together a very com prehensive book on fuzzy graphs and fuzzy hypergraphs. Fuzzy graphs and fuzzy hypergraphs studies in fuzziness and. Fuzzy influence graphs new mathematics and natural computation. Fuzzy hypergraphs and fuzzy intersection graphs dtic. We have shown that the removal of a fuzzy bridge from a fuzzy magic cycle with odd nodes reduces the strength of a fuzzy magic cycle. Pdf it is the case that, in certain applications of fuzzy graphs, a tnorm, instead of a minimum, is more suitable. Fuzzy mathematics forms a branch of mathematics related to fuzzy set theory and fuzzy logic.
Graph theory has numerous applications in modern sciences and technology. Professors mordeson and nair have made a real contribution in putting. Application to cluster analysis clusters based on distance and connectivity fuzzy graphs in fuzzy neural networks fuzzy graphs in database theory fuzzy decision trees. Nair fuzzy graphs and fuzzy hypergraphs with 29 figures and 10 tables physicaverlag a springerverlag company. In the course of fuzzy technological development, fuzzy graph theory was identified quite early on for its importance in making things work. The complement of a fuzzy graph was proposed by mordeson and peng 9mordeson jn. Nair, fuzzy graphs and fuzzy hypergraphs, physica verlag, 2000. Fuzzy graphs and fuzzy hypergraphs pdf free download epdf. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. Nair, fuzzy graphs and fuzzy hypergraphs, physicaverlag, 2000. The fuzzy relations between two fuzzy sets were also considered by rosenfeld 11 and developed the structure of fuzzy graphs, obtained analogous of several graph theoretical concepts.
Main termsvector search result for fuzzy hypergraphs 1. 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. Further, we define the spike reduction and sequentially simple qrung orthopair fuzzy directed hypergraphs. Professors mordeson and nair have created such a volume which enables engineers and design ers.
Bhutani and battou 10 introduced the concept of mstrong fuzzy graphs with some properties. Nair, fuzzy graphs and fuzzy hypergraphs, new york. We also generalize the vertex coloring lemma of berge, providing a characterization of the family of all minimal fuzzy transversals of a fuzzy hypergraph. A study on hypergraph representations of complex fuzzy. Vertex connectivity of fuzzy graphs with applications to. Mordeson and premchand nair 1 introduced the concept of fuzzy hypergraphs and several fuzzy analogs of hypergraph theory. A graph is a pair v, r, where v is a set and r is a relation on v. Fuzzy graphs and fuzzy hypergraphs studies in fuzziness. Mordeson is the author of fuzzy graphs and fuzzy hypergraphs 4. The last section deals with the conclusions and future directions. Vijaya department of mathematics, marudupandiyar college, thanjavur, tamil nadu, india 6403 abstract in this work we introduce the complement of strong fuzzy graph, tensor product of fuzzy graphs and strong fuzzy graph. Fuzzy influence graphs new mathematics and natural. Mordeson and nair presented a valuable contribution on fuzzy graphs as well as fuzzy hypergraphs in 12. Complement properties of tensor product of strong fuzzy.
Vijaya kumar, some metric aspects of fuzzy graphs, in proceedings of the conference on graph connections, allied publishers 1999 111114. Thesis on studies on fuzzy graphs, cochin university of science and technology. It is proved that every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced. However, there are relatively books available on the very same topic.
Mordeson, connectivity concepts in fuzzy incidence graphs, information sciences 382383 2017 326333. Pdf in this paper the concept of effective fuzzy graph is defined and the. We have also shown how the fuzzy analog satisfies the properties of the 6x6 matrix of the riemann tensor by expressing it as a union of the fuzzy complete graph formed by. Mathematical model by fuzzy rules from dominating graphs. It started in 1965 after the publication of lotfi asker zadehs seminal work fuzzy sets. Fuzzy graphs and fuzzy hypergraphs by john n mordeson, 9783662003909, available at book depository with free delivery worldwide. Jesintha rosline, characterization of fuzzy graphs into. Novel applications of mpolar fuzzy hypergraphs ios press.
Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined. Borzooei, vulnerability and government response to human trafficking. Later, bhattacharya 5 gave some remarks on fuzzy graphs, and some operations on fuzzy graphs were introduced by mordeson and peng 19. We present some applications of mpolar fuzzy hypergraphs in planet surface networks, social networks and grouping of incompatible chemical substances. Pdf cyclic symmetry of riemann tensor in fuzzy graph theory. We first summarize some basic definitions, most of which can be found in. We have developed a fuzzy graphtheoretic analog of the riemann tensor and have analyzed its properties. In particular, the discussion on hypergraphs certainly is an innovative idea. The natural extension of this research work is the application of intervalvalued fuzzy graphs in the area of soft computing including neural networks, expert systems, database theory, and geographical information systems. Zimmermann 4 has discussed some properties of fuzzy graphs. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. Intervalvalued fuzzy hypergraphs were introduced by chen. In this paper, we discuss some properties of the self complement and self weak complement bipolar fuzzy graphs, and get a sufficient condition for a bipolar fuzzy graph to be the self weak complement bipolar fuzzy graph.
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