Vijaya kumar, some metric aspects of fuzzy graphs, in proceedings of the conference on graph connections, allied publishers 1999 111114. A graph is a pair v, r, where v is a set and r is a relation on v. Bhattacharya gave some remarks on fuzzy graphs in 5. Kaufmann 7 presented the idea of fuzzy hypergraphs. Graph theory has numerous applications in modern sciences and technology. Bhutani and rosenfeld introduced the concept of mstrong fuzzy graphs in 7 and studied. An application to the problem concerning group structure connectedness of a fuzzy graph 4. Nair fuzzy graphs and fuzzy hypergraphs with 29 figures and 10 tables physicaverlag a springerverlag company.
Fuzzy influence graphs new mathematics and natural. Pdf cyclic symmetry of riemann tensor in fuzzy graph theory. This function is also called a membership function. Professors mordeson and nair have made a real contribution in putting together a very com prehensive book on fuzzy graphs and fuzzy hypergraphs.
Bhutani and battou 10 introduced the concept of mstrong fuzzy graphs with some properties. Later, bhattacharya 5 gave some remarks on fuzzy graphs, and some operations on fuzzy graphs were introduced by mordeson and peng 19. In section 4, we discuss how the concept of qrung orthopair fuzzy directed hypergraphs can be applied to analyze the real life problems. Rosenfeld 11 discussed the concept of fuzzy graphs whose basic idea was introduced by kauffmann 8. A description of strengthening and weakening members of a group 3. Category of p om lfuzzy graphs and hypergraphs 53 it is obvious that. The complement of a fuzzy graph was proposed by mordeson and peng 9mordeson jn. Professors mordeson and nair have created such a volume which enables engineers and design ers. It is proved that every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. 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. We also generalize the vertex coloring lemma of berge, providing a characterization of the family of all minimal fuzzy transversals of a fuzzy hypergraph. Graph theory has numerous application to problems in systems analysis, operations research, economics, and transportation.
Main termsvector search result for fuzzy hypergraphs 1. We first summarize some basic definitions, most of which can be found in. Mathematical model by fuzzy rules from dominating graphs. Nair, fuzzy graphs and fuzzy hypergraphs physica verlag, heidelberg 1998. 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. Professors mordeson and nair have made a real contribution in putting.
Fuzzy mathematics forms a branch of mathematics related to fuzzy set theory and fuzzy logic. 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. Vague fuzzy incidence graphs, new mathematics and natural computation 14 2 2018 203219. In the course of fuzzy technological development, fuzzy graph theory was identified quite early on for its importance in making things work. A fuzzy subgraph h of g is defined by a fuzzy subset. Thesis on studies on fuzzy graphs, cochin university of science and technology.
Nair, fuzzy graphs and fuzzy hypergraphs, physica verlag publication, heidelbserg, second edition 2001. Jesintha rosline, characterization of fuzzy graphs into. Fuzzy graphs and fuzzy hypergraphs studies in fuzziness. Mordeson and nair presented a valuable contribution on fuzzy graphs as well as fuzzy hypergraphs in 12. Nair, fuzzy graphs and fuzzy hypergraphs, new york.
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. Nair, fuzzy graphs and fuzzy hypergraphs, physica verlag, 2000. A study on hypergraph representations of complex fuzzy. Nagoor gani and radha 16 described some properties of. Pdf in this paper the concept of effective fuzzy graph is defined and the. Nair, fuzzy graphs and fuzzy hypergraphs, physicaverlag, 2000. Application to cluster analysis clusters based on distance and connectivity fuzzy graphs in fuzzy neural networks fuzzy graphs in database theory fuzzy decision trees.
Mordeson, connectivity concepts in fuzzy incidence graphs, information sciences 382383 2017 326333. 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. 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. In this paper we are giving an overview on the fuzzy graph and its various kinds. 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. 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. Vertex connectivity of fuzzy graphs with applications to. Some results on point set domination of fuzzy graphs in. In this paper, the novel concept of dombi fuzzy graph is introduced.
Malarvizhi discussed the isomorphism between fuzzy graphs and some properties of. We have developed a fuzzy graphtheoretic analog of the riemann tensor and have analyzed its properties. Fuzzy influence graphs new mathematics and natural computation. Certain concepts of bipolar fuzzy directed hypergraphs. Fuzzy hypergraphs and fuzzy intersection graphs dtic. Operations on intuitionistic fuzzy graph structures sciencedirect. Mordeson and premchand nair 1 introduced the concept of fuzzy hypergraphs and several fuzzy analogs of hypergraph theory. 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. Fuzzy graphs and fuzzy hypergraphs studies in fuzziness and. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. Fuzzy graphs and fuzzy hypergraphs by john n mordeson, 9783662003909, available at book depository with free delivery worldwide. Intervalvalued fuzzy hypergraphs were introduced by chen.
Borzooei, vulnerability and government response to human trafficking. Complement and isomorphism on bipolar fuzzy graphs. Fuzzy set theoryand its applications, fourth edition. Fuzzy graphs and fuzzy hypergraphs pdf free download epdf. Mordeson is the author of fuzzy graphs and fuzzy hypergraphs 4. The last section deals with the conclusions and future directions. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced. However, there are relatively books available on the very same topic. Zimmermann 4 has discussed some properties of fuzzy graphs. In the course of fuzzy technological development, fuzzy graph theory was identified quite. Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined.
Also we investigate relations between operations union, join, and complement on bipolar fuzzy graphs. In this paper, we define a graphtheoretic analog for the riemann tensor and analyze properties of the cyclic symmetry. Also it is proved that the effective edge coloring of a fuzzy graph g is not. Pal 2012, bipolar fuzzy hypergraphs, international. In particular, the discussion on hypergraphs certainly is an innovative idea. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. Further, we define the spike reduction and sequentially simple qrung orthopair fuzzy directed hypergraphs. Pdf it is the case that, in certain applications of fuzzy graphs, a tnorm, instead of a minimum, is more suitable. It started in 1965 after the publication of lotfi asker zadehs seminal work fuzzy sets. We present some applications of mpolar fuzzy hypergraphs in planet surface networks, social networks and grouping of incompatible chemical substances. 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.
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