On Bipolar Single Valued Neutrosophic Graphs

In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.

[1]  Hong-yu Zhang,et al.  An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multi-criteria Decision-making Problems , 2015, Int. J. Comput. Intell. Syst..

[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]  I. Turksen Interval valued fuzzy sets based on normal forms , 1986 .

[4]  Gaurav,et al.  Hybrid model for medical diagnosis using Neutrosophic Cognitive Maps with Genetic Algorithms , 2015, 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[5]  A. Rajkumar,et al.  A Study on Miracles through Holy Bible using Neutrosophic Cognitive Maps (NCMS) , 2013 .

[6]  Jun Ye,et al.  Single-Valued Neutrosophic Minimum Spanning Tree and Its Clustering Method , 2014, J. Intell. Syst..

[7]  F. Smarandache,et al.  Interval Valued Neutrosophic Graphs , 2016 .

[8]  Florentin Smarandache,et al.  On Strong Interval Valued Neutrosophic Graphs , 2016 .

[9]  D. Ezhilmaran,et al.  Morphism of bipolar intuitionistic fuzzy graphs , 2015 .

[10]  Muhammad Akram,et al.  m-polar fuzzy graphs and m-polar fuzzy line graphs , 2017 .

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

[12]  A. Mohamed Ismayil,et al.  On Strong Interval-Valued Intuitionistic Fuzzy Graph , 2014 .

[13]  Rajshekhar Sunderraman,et al.  Single Valued Neutrosophic Sets , 2010 .

[14]  A. Vince,et al.  n-Graphs , 1988, Discret. Math..

[15]  Heng-Da Cheng,et al.  A NEW NEUTROSOPHIC APPROACH TO IMAGE THRESHOLDING , 2008 .

[16]  Xiuwu Liao,et al.  On single valued neutrosophic relations , 2015, J. Intell. Fuzzy Syst..

[17]  Muhammad Akram Interval-valued fuzzy line graphs , 2011, Neural Computing and Applications.

[18]  Florentin Smarandache,et al.  Bipolar neutrosophic sets and their application based on multi-criteria decision making problems , 2015, 2015 International Conference on Advanced Mechatronic Systems (ICAMechS).

[19]  Yanqing Zhang,et al.  Truth-value based interval neutrosophic sets , 2005, 2005 IEEE International Conference on Granular Computing.

[20]  S. Begum Degree, Order and Size in Intuitionistic Fuzzy Graphs , 2010 .

[21]  Swati Aggarwal,et al.  Neutrosophic modeling and control , 2010, 2010 International Conference on Computer and Communication Technology (ICCCT).

[22]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[23]  Swati Aggarwal,et al.  Extension to fuzzy logic representation: Moving towards neutrosophic logic - A new laboratory rat , 2013, 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[24]  Florentin Smarandache,et al.  Single valued neutrosophic graphs: Degree, order and size , 2016, 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[25]  Florentin Smarandache,et al.  New distance and similarity measures of interval neutrosophic sets , 2014, 17th International Conference on Information Fusion (FUSION).

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

[27]  A. Gani,et al.  On Irregular Fuzzy Graphs , 2012 .

[28]  Jun Ye,et al.  Trapezoidal neutrosophic set and its application to multiple attribute decision-making , 2014, Neural Computing and Applications.

[29]  Florentin Smarandache,et al.  Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies , 2015 .

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

[31]  Jun Ye Vector Similarity Measures of Simplified Neutrosophic Sets and Their Application in Multicriteria Decision Making , 2014 .

[32]  Florentin Smarandache,et al.  Neutrosophic set - a generalization of the intuitionistic fuzzy set , 2004, 2006 IEEE International Conference on Granular Computing.

[33]  Shenggang Li,et al.  m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets , 2014, TheScientificWorldJournal.

[34]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[35]  Hong-yu Zhang,et al.  An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets , 2015, Neural Computing and Applications.

[36]  P. Bahr,et al.  Sampling: Theory and Applications , 2020, Applied and Numerical Harmonic Analysis.

[37]  Muhammad Akram,et al.  Interval-valued fuzzy graphs , 2012, Comput. Math. Appl..

[38]  Florentin Smarandache,et al.  Complex neutrosophic set , 2016, Neural Computing and Applications.

[39]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[40]  Florentin Smarandache,et al.  The theory of neutrosophic cubic sets and their applications in pattern recognition , 2016, J. Intell. Fuzzy Syst..

[41]  Swati Aggarwal,et al.  Neutrosophic classifier: An extension of fuzzy classifer , 2014, Appl. Soft Comput..

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

[43]  W. B. Vasantha Kandasamy,et al.  Neutrosophic Graphs: A New Dimension to Graph Theory , 2015 .