Novel concepts of bipolar fuzzy competition graphs

A fuzzy graph theory is one of the most developing area of research, which has a variety of applications in different fields, including computer science, communication networks, social networks, decision-making and optimization problems. In this research article, we present various methods of construction of bipolar fuzzy competition graphs. We investigate some novel properties of bipolar fuzzy competition graphs. We present an interesting application of bipolar fuzzy competition graphs in politics. We also design an algorithm for computing the strength of competition among political candidates in a local government.

[1]  Frank Harary,et al.  Graph Theory , 2016 .

[2]  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.

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

[4]  Sunil Mathew,et al.  Strongest Strong Cycles and $\theta$-Fuzzy Graphs , 2013, IEEE Transactions on Fuzzy Systems.

[5]  Zeshui Xu.  Additive Intuitionistic Fuzzy Aggregation Operators Based on Fuzzy Measure , 2016, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[6]  Muhammad Akram,et al.  Bipolar Fuzzy Competition Graphs , 2015, Ars Comb..

[7]  Azriel Rosenfeld,et al.  Strong arcs in fuzzy graphs , 2003, Inf. Sci..

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

[9]  Muhammad Akram,et al.  Bipolar fuzzy graphs with applications , 2013, Knowl. Based Syst..

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

[11]  Muhammad Akram,et al.  Certain types of irregular m-polar fuzzy graphs , 2017 .

[12]  Prabir Bhattacharya,et al.  Some remarks on fuzzy graphs , 1987, Pattern Recognit. Lett..

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

[14]  吳森原,et al.  The Compositions of Fuzzy Digraphs , 1986 .

[15]  Sunil Mathew,et al.  Types of arcs in a fuzzy graph , 2009, Inf. Sci..

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

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

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

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

[20]  Kenneth H. Rosen,et al.  Discrete Mathematics and its applications , 2000 .

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

[22]  Sankar Sahoo,et al.  Intuitionistic fuzzy competition graphs , 2016 .

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

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

[25]  A. Somasundaram.  Domination in products of fuzzy graphs , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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