Bipolar Fuzzy Graphs with Categorical Properties

AbstractTheoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. In this paper, we discussed some properties of the µ–complement of bipolar fuzzy graphs. Self µ–complement bipolar fuzzy graphs and self weak µ–complement bipolar fuzzy graphs are defined and a necessary condition for a bipolar fuzzy graph to be self µ–complement is given. We defined busy vertices and free vertices in bipolar fuzzy graphs and studied their image under an isomorphism. Categorical properties of bipolar fuzzy graphs are discussed. Also, we investigated some properties of isomorphism on bipolar fuzzy graphs.

[1]  Jiancheng Zhang,et al.  Some properties of fuzzy reasoning in propositional fuzzy logic systems , 2010, Inf. Sci..

[2]  Madhumangal Pal,et al.  Fuzzy Planar Graphs , 2015, IEEE Transactions on Fuzzy Systems.

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

[4]  Muhammad Akram,et al.  $$m$$m-Step fuzzy competition graphs , 2015 .

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

[6]  Madhumangal Pal,et al.  Fuzzy colouring of fuzzy graphs , 2016 .

[7]  A. Nagoorgani,et al.  FREE NODES AND BUSY NODES OF A FUZZY GRAPH , 2006 .

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

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

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

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

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

[13]  Kiran R. Bhutani,et al.  On automorphisms of fuzzy graphs , 1989, Pattern Recognit. Lett..

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

[15]  Reinhard Diestel,et al.  Locally finite graphs with ends: A topological approach, II. Applications , 2010, Discret. Math..

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

[17]  V. Novák.  Fuzzy sets and their applications , 1989 .

[18]  Reinhard Diestel,et al.  Locally finite graphs with ends: A topological approach, I. Basic theory , 2009, Discret. Math..

[19]  Juan Lu,et al.  Categorical properties of M-indiscernibility spaces , 2011, Theor. Comput. Sci..

[20]  R. Bruce Richter,et al.  Graph-like spaces: An introduction , 2011, Discret. Math..

[21]  Péter Komjáth,et al.  The quasi order of graphs on an ordinal , 2011, Discret. Math..

[22]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

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

[24]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[25]  J. Hopfield.  Neurons withgraded response havecollective computational properties likethoseoftwo-state neurons , 1984 .

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

[27]  Madhumangal Pal,et al.  Irregular Bipolar Fuzzy Graphs , 2012, ArXiv.

[28]  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.

[29]  Madhumangal Pal.  Fuzzy Tolerance Graph , 2012 .

[30]  Muhammad Akram,et al.  Regular bipolar fuzzy graphs , 2011, Neural Computing and Applications.

[31]  K. Srinivasa Rao,et al.  On the Latest Times and Float Times of Activities in a Fuzzy Project Network with LR Fuzzy Numbers , 2012, Int. J. Fuzzy Syst. Appl..

[32]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .