Main Article Content
Abstract
Keywords
Article Details
References
- References
- M. Akram, Bipolar fuzzy graphs, Information Sciences 181(24) (2011) 5548-5564.
- M. Akram, M. Sarwar, Novel multiple criteria decision making methods based on bipolar
- neutrosophic sets and bipolar neutrosophic graphs, viXra:1701.0190, 2015.
- M. Akram and S. Shahzadi, Neutrosophic soft graphs with application, Journal of Intelligent
- & Fuzzy Systems, 32(1)(2017) 841-858.
- N.O. Al-Shehrie and M. Akram, Bipolar fuzzy competition graphs, Ars Combinatoria 121
- (2015) 385-402.
- M. Akram and M. Nasir, Competition graphs in bipolar neutrosophic environment, 2017.
- H.H. Cho, S.-R. Kim and Y. Nam, The m-step competition graph of a digraph, Discrete
- Applied Mathematics 105 (2000) 115-127.
- P. Bhattacharya, Some remark on fuzzy graphs, Pattern Recognition Letters 6 (1987)
- -302.
- S. Broumi, M. Talea, A. Bakali and F. Smarandache, On bipolar single valued neutrosophic
- graphs, New Trends in Neutrosophic Theory and Applications (2016) 203-221.
- J.E. Cohen, Interval graphs and food webs: a finding and a problems, Document 17696-
- PR, RAND Corporation, Santa Monica, CA (1968).
- I. Deli, M. Ali and F. Smarandache, (2015), Bipolar neutrosophic sets and their applications
- based on multi-criteria decision making problems, In Advanced Mechatronic Systems
- (ICAMechS), International Conference IEEE, 249-254.
- R. Dhavaseelan, R. Vikramaprasad and V. Krishnaraj, Certain types of neutrosophic
- graphs, International Journal of Mathematics Science and Applications 5(2) (2015) 333-
- A. Kauffman, Introduction a la theorie des sousemsembles flous, Masson et cie Paris
- (1973).
- A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Application (L.A. Zadeh, K.S. Fu, M.
- Shimura Eds.) Academic press New York (1975) 77-95.
- S. Samanta and M. Pal, Fuzzy k-competition graphs and p-competition fuzzy graphs,
- Fuzzy Information and Engineering 5 (2013) 191-204.
- S. Samanta, M. Akram and M. Pal, m-Step fuzzy competition graphs, Journal of Applied
- Mathematics and Computing 47(2015) 461-472.
- M. Sarwar and M. Akram, Novel concepts of bipolar fuzzy competition graphs, Journal
- of Applied Mathematics and Computing (2016) DOI 10.1007/s12190-016-1021-z.
- M. Nasir, S. Siddique and M. Akram, Novel properties of intuitionistic fuzzy competition
- graphs, Journal of Uncertain Systems 2(1)(2017) 49-67.
- F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Granular
- Computing, 2006, IEEE International Conference (2006) 38-42 DOI:10.1109/GRC
- F. Smarandache, A geometric interpretation of the neutrosophic set- A generalization of
- the intuitionistic fuzzy set, Granular Computing, (GrC), 2011 IEEE International Conference
- (2011) 602-606 DOI:10.1109/GRC.2011.6122665.
- F. Smarandache, Types of neutrosophic graphs and neutrosophic algebraic structures
- together with their applications in technology, Seminar, Universitatea Transilvania din
- Brasov, Facultatea de Design de Produs si Mediu, Brasov, Romania 06 June (2015).
- H. Wang, F. Smarandache, Y. Zhang and R. Sunderraman, Single valued neutrosophic
- sets, Multisapace and Multistructure 4 (2010) 410-413.
- S.Y. Wu, The compositions of fuzzy digraphs, Journal of Research in Education Science,
- (1986) 603-628.
- J. Ye, Single-valued neutrosophic minimum spanning tree and its clustering method, Journal
- of Intelligent Systems 23(3)(2014) 311-324.
- J. Ye, A multicriteria decision-making method using aggregation operators for simplified
- neutrosophic sets, Journal of Intelligent & Fuzzy Systems 26(5) (2014) 2459-2466.
- L.A. Zadeh, Fuzzy sets, Information and Control 08 (1965) 338-353.
- W.-R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive
- modeling and multiagent decision analysis, In: Proceedings of IEEE Conference Fuzzy
- Information Processing Society Biannual Conference (1994) 305-309.
References
References
M. Akram, Bipolar fuzzy graphs, Information Sciences 181(24) (2011) 5548-5564.
M. Akram, M. Sarwar, Novel multiple criteria decision making methods based on bipolar
neutrosophic sets and bipolar neutrosophic graphs, viXra:1701.0190, 2015.
M. Akram and S. Shahzadi, Neutrosophic soft graphs with application, Journal of Intelligent
& Fuzzy Systems, 32(1)(2017) 841-858.
N.O. Al-Shehrie and M. Akram, Bipolar fuzzy competition graphs, Ars Combinatoria 121
(2015) 385-402.
M. Akram and M. Nasir, Competition graphs in bipolar neutrosophic environment, 2017.
H.H. Cho, S.-R. Kim and Y. Nam, The m-step competition graph of a digraph, Discrete
Applied Mathematics 105 (2000) 115-127.
P. Bhattacharya, Some remark on fuzzy graphs, Pattern Recognition Letters 6 (1987)
-302.
S. Broumi, M. Talea, A. Bakali and F. Smarandache, On bipolar single valued neutrosophic
graphs, New Trends in Neutrosophic Theory and Applications (2016) 203-221.
J.E. Cohen, Interval graphs and food webs: a finding and a problems, Document 17696-
PR, RAND Corporation, Santa Monica, CA (1968).
I. Deli, M. Ali and F. Smarandache, (2015), Bipolar neutrosophic sets and their applications
based on multi-criteria decision making problems, In Advanced Mechatronic Systems
(ICAMechS), International Conference IEEE, 249-254.
R. Dhavaseelan, R. Vikramaprasad and V. Krishnaraj, Certain types of neutrosophic
graphs, International Journal of Mathematics Science and Applications 5(2) (2015) 333-
A. Kauffman, Introduction a la theorie des sousemsembles flous, Masson et cie Paris
(1973).
A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Application (L.A. Zadeh, K.S. Fu, M.
Shimura Eds.) Academic press New York (1975) 77-95.
S. Samanta and M. Pal, Fuzzy k-competition graphs and p-competition fuzzy graphs,
Fuzzy Information and Engineering 5 (2013) 191-204.
S. Samanta, M. Akram and M. Pal, m-Step fuzzy competition graphs, Journal of Applied
Mathematics and Computing 47(2015) 461-472.
M. Sarwar and M. Akram, Novel concepts of bipolar fuzzy competition graphs, Journal
of Applied Mathematics and Computing (2016) DOI 10.1007/s12190-016-1021-z.
M. Nasir, S. Siddique and M. Akram, Novel properties of intuitionistic fuzzy competition
graphs, Journal of Uncertain Systems 2(1)(2017) 49-67.
F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Granular
Computing, 2006, IEEE International Conference (2006) 38-42 DOI:10.1109/GRC
F. Smarandache, A geometric interpretation of the neutrosophic set- A generalization of
the intuitionistic fuzzy set, Granular Computing, (GrC), 2011 IEEE International Conference
(2011) 602-606 DOI:10.1109/GRC.2011.6122665.
F. Smarandache, Types of neutrosophic graphs and neutrosophic algebraic structures
together with their applications in technology, Seminar, Universitatea Transilvania din
Brasov, Facultatea de Design de Produs si Mediu, Brasov, Romania 06 June (2015).
H. Wang, F. Smarandache, Y. Zhang and R. Sunderraman, Single valued neutrosophic
sets, Multisapace and Multistructure 4 (2010) 410-413.
S.Y. Wu, The compositions of fuzzy digraphs, Journal of Research in Education Science,
(1986) 603-628.
J. Ye, Single-valued neutrosophic minimum spanning tree and its clustering method, Journal
of Intelligent Systems 23(3)(2014) 311-324.
J. Ye, A multicriteria decision-making method using aggregation operators for simplified
neutrosophic sets, Journal of Intelligent & Fuzzy Systems 26(5) (2014) 2459-2466.
L.A. Zadeh, Fuzzy sets, Information and Control 08 (1965) 338-353.
W.-R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive
modeling and multiagent decision analysis, In: Proceedings of IEEE Conference Fuzzy
Information Processing Society Biannual Conference (1994) 305-309.