Document Type: Research Paper


1 Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

2 Department of Applied Mathematics, Xi'an University of Posts, and Telecommunications, Xi'an, China

3 Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran and Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

4 Faculty of Mathematics, Al.I.Cuza University, 700506 Iasi, Romania


In this research study, we present a novel frame work for handling bipolar fuzzy soft information by combining bipolar fuzzy soft sets with graphs.
We introduce several basic notions concerning bipolar fuzzy soft graphs and investigate some related properties.
We also consider the application of the bipolar fuzzy soft graphs. In particular, three efficient algorithms are developed to solve multiple criteria decision-making problems regarding social network, investment in shares and detection of bipolar disorder in children.


[1] S. Abdullah, M. Aslam and K. Ullah, Bipolar fuzzy soft sets and its applications in decision
making problem, Journal of Intelligent and Fuzzy Systems, 27(2) (2014), 729-742.
[2] H. Aktas and N. Cagman, Soft sets and soft groups, Information Sciences, 177 (2007), 2726-
[3] M. Akram, Bipolar fuzzy graphs, Information Sciences 181 (2011), 5548{5564.
[4] M. Akram, Bipolar fuzzy graphs with applications, Knowledge Based Systems, 39 (2013), 1-8.
[5] M. Akram, and S. Nawaz, Operations on soft graphs, Fuzzy Information and Engineering, 7
(2015), 423{449.
[6] M. Akram, and S. Nawaz, On fuzzy soft graphs, Italian journal of pure and applied mathe-
matics 34 (2015), 497{514.
[7] M. Akram and S. Nawaz, Fuzzy soft graphs with applications, Journal of intelligent and fuzzy
systems, 30 (2016), 3619{3632.
[8] M. Akram, Bipolar fuzzy soft Lie algebras, Quasigroups and Related Systems, 21 (2013),
[9] T. Al-Hawary, Complete fuzzy graphs, International Journal of Mathematical Combinatorics,
4 (2011), 26-34.
[10] J. C. R. Alcantud, A novel algorithm for fuzzy soft set based decision making from multiob-
server input parameter data set, Information Fusion 29 (2016), 142-148.
[11] J. C. R. Alcantud,, Some formal relationships among soft sets, fuzzy sets, and their exten-
sions, International Journal of Approximate Reasoning, 68 (2016), 45-53.
[12] M.I. Ali, F. Feng, X. Y. Liu, W. K. Min and M. Shabir, On some new operations in soft set
theory, Computers and Mathematics with Applications, 57 (2009), 1547{1553.
[13] K. V. Babitha and J. J. Sunil, Soft set relations and functions, Computers and Mathematics
with Applications, 60 (2010), 1840{1849.
[14] P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognition Letter, 6 (1987), 297-
[15] N. Cagman, S. Enginoglu and F. Citak, Fuzzy soft set theory and its applications, Iranian
Journal of Fuzzy Systems, 8(3) (2011), 137-147.
[16] F. Feng, X. Y. Liu, V. Leoreanu-Fotea and Y. B. Jun, Soft sets and soft rough sets, Informa-
tion Sciences, 181 (2011), 1125{1137.
[17] F. Feng, C. X. Li, B. Davvaz and M. Irfan Ali, Soft sets combined with fuzzy sets and rough
sets: a tentative approach, Soft Computing, 14 (2010), 899{911.

[18] F. Feng, Y. B. Jun, X. Y. Liu and L. F. Li, An adjustable approach to fuzzy soft set based
decision making, Journal of Computational and Applied Mathematics, 234 (2010), 10{20.
[19] F. Feng and W. Pedrycz, On scalar products and decomposition theorems of fuzzy soft sets,
Journal of Multi-valued Logic and Soft Computing, 25 (2015), 45-80.
[20] A. Kauffman, Introduction a la Theorie des Sous-emsembles Flous, Masson et Cie, ISBN
2-225-45804-9, 1 (1977), 31.
[21] P. K. Maji, A. R. Roy and R. Biswas, Fuzzy soft sets, Journal of fuzzy Mathematics, 9(3)
(2001), 589-602.
[22] S. Mathew and M. Sunitha, Types of arcs in a fuzzy graph, Information Sciences, 179(11)
(2009), 1760-1768.
[23] S. Mathew and M. Sunitha, Strongest strong cycles and fuzzy graphs, Fuzzy Systems, IEEE
Transactions on, 21 (2013),1096-1104.
[24] J. N. Mordeson and C. S. Peng, Operations on fuzzy graphs, Information Sciences, 79 (1994),
[25] J. N. Mordeson and P. S. Nair, Fuzzy graphs and fuzzy hypergraphs, Physica Verlag, Heidel-
berg, ISBN 978-3-7908-1854-3, 2001.
[26] D. A. Molodtsov, Soft set theory- first results, Computers and Mathematics with Applications,
37 (1999), 19{31.
[27] H. Rashmanlou, S. Samanta, M. Pal and R. A. Borzooei, Bipolar fuzzy graphs with categorical
properties, International Journal of Computational Intelligence Systems, 8(5) (2015), 808-818
[28] A. Rosenfeld, Fuzzy graphs, in: L.A. Zadeh, K.S. Fu and M. Shimura (Eds.), Fuzzy Sets and
Their Applications, Academic Press, New York, (1975), 77-95.
[29] A. R. Roy and P. K. Maji, A fuzzy soft set theoretic approach to decision making problems,
Journal of Comput. Appl. Math., 203 (2007), 412-418.
[30] M. Sarwar and M. Akram , Novel concepts bipolar fuzzy competition graphs, Journal of
Applied Mathematics and Computing, 54(1-2) (2017), 511-547.
[31] S. Shahzadi and M Akram, Intuitionistic fuzzy soft graphs with applications, Journal of
Applied Mathematics and Computing, 55(1-2) (2017), 369-392.
[32] S. Shahzadi and M. Akram, Edge regular intuitionistic fuzzy soft graphs, Journal of Intelligent
& Fuzzy Systems, 31(3) (2016), 1881-1895.
[33] P. K. Singh and A. Ch. Kumar, Bipolar fuzzy graph representation of concept lattice, Infor-
mation Sciences, 288 (2014), 437-448.
[34] P. K. Singh and A. Ch. Kumar, A note on bipolar fuzzy graph representation of concept
lattice, International Journal of Computing Science and Mathematics, 5(4) (2014), 381-393.
[35] M.S. Sunitha and A. Vijayakumar, Complement of a fuzzy graph, Indian Journal of Pure and
Applied Mathematics, 33(9) (2002) 1451-1464.
[36] H. L. Yang, S. G. Li, W. H. Yang and Y. Lu, Notes on bipolar fuzzy graphs", Information
Sciences, 242 (2013), 113-121.
[37] H. L. Yang, S. G. Li, Z. L. Guo, and C.􀀀H. Ma, Transformation of bipolar fuzzy rough set
models, Knowledge-Based Systems, 27 (2012), 60-68.
[38] L. A. Zadeh, Fuzzy sets, Information and control, 8(3) (1965), 338-353.
[39] L. A. Zadeh, Similarity relations and fuzzy orderings. Information sciences, 3(2), 1971, 177-
[40] W. R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive
modeling and multiagent decision analysis, In Fuzzy Information Processing Society Biannual
Conference, 1994.
Industrial Fuzzy Control and Intelligent Systems Conference, and the NASA Joint Technology
Workshop on Neural Networks and Fuzzy Logic, IEEE 1994, 305-309.