Product of bipolar fuzzy graphs and their degree

The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theory is successfully used in many problems. A bipolar fuzzy set is a generalization of the fuzzy set. In this paper, two new operations on bipolar fuzzy graphs, viz. normal product and tensor product, are defined. Also, the degrees of the vertices of the resultant graphs which are obtained from two given bipolar fuzzy graphs and using the operations Cartesian product, composition, tensor and normal product are determined.

[1]  M. Naga Maruthi Kumari,et al.  Isomorphism On Interval-Valued Fuzzy Graphs , 2016 .

[2]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[3]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[4]  John N. Mordeson,et al.  Operations on Fuzzy Graphs , 1994, Inf. Sci..

[5]  Keon-Myung Lee,et al.  Comparison of Interval-valued fuzzy sets, Intuitionistic fuzzy sets, and bipolar-valued fuzzy sets , 2004 .

[6]  Madhumangal Pal,et al.  Fuzzy k-competition graphs and p-competition fuzzy graphs , 2013 .

[7]  G. Nirmala,et al.  FUZZY GRAPHS ON COMPOSITION, TENSOR AND NORMAL PRODUCTS , 2012 .

[8]  Madhumangal Pal,et al.  New concepts of fuzzy planar graphs , 2014 .

[9]  Madhumangal Pal,et al.  Interval-valued fuzzy planar graphs , 2016, Int. J. Mach. Learn. Cybern..

[10]  Madhumangal Pal,et al.  Antipodal Interval-Valued Fuzzy Graphs , 2014, ArXiv.

[11]  Madhumangal Pal,et al.  Fuzzy Threshold Graphs , 2011 .

[12]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[13]  Young Bae Jun,et al.  Complete interval-valued fuzzy graphs , 2013 .

[14]  G. Geetha Ramani,et al.  Product Intuitionistic Fuzzy Graph , 2011 .

[15]  Wen-Ran Zhang,et al.  Bipolar Fuzzy Sets , 1997 .

[16]  Muhammad Akram,et al.  Bipolar fuzzy graphs , 2011, Inf. Sci..

[17]  Madhumangal Pal,et al.  Bipolar Fuzzy Hypergraphs , 2012 .

[18]  Madhumangal Pal,et al.  A study on bipolar fuzzy graphs , 2015, J. Intell. Fuzzy Syst..

[19]  Madhumangal Pal,et al.  Some more results on fuzzy k-competition graphs , 2014 .

[20]  K. Radha.  The Degree of a Vertex in some Fuzzy Graphs , 2009 .

[21]  Talebi.  Some Operations on Vague Graphs , 2014 .

[22]  Wen-Ran Zhang,et al.  Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis , 1994, NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige.

[23]  John N. Mordeson,et al.  Fuzzy Graphs and Fuzzy Hypergraphs , 2000, Studies in Fuzziness and Soft Computing.

[24]  Young Bae Jun,et al.  Some operations on bipolar fuzzy graphs , 2014 .

[25]  Madhumangal Pal,et al.  Some Properties of Highly Irregular Interval Valued Fuzzy Graphs , 2013 .

[26]  Madhumangal Pal,et al.  Telecommunication System Based on Fuzzy Graphs , 2014 .