Hypergraphs are the basis of various techniques which are widely used in modern mathematics. There are many complex phenomena and concepts in many areas, including rewriting systems, problem solving, databases and logic programming which can be represented using hypergraphs. Our main objective in this research paper is to generalize the concept of bipolar neutrosophic sets to hypergraphs. We introduce certain new concepts, including bipolar neutrosophic hypergraphs, elementary, sectionally elementary and B-tempered bipolar neutrosophic hypergraphs. We describe the concepts of transversals, minimal transversals and locally minimal transversals of bipolar neutrosophic hypergraphs and discuss their certain properties. We also develop and implement algorithm for finding minimal bipolar neutrosophic transversals. Further, we present some applications of bipolar neutrosophic hypergraphs in marketing and biology.
AkramM., Bipolar fuzzy graphs, Information Sciences181(24) (2011), 5548–5564.
2.
AkramM. and SarwarM., Novel multiple criteria making methods based on bipolar neutrosophic sets and bipolar neutrosophic graphs, Italian Journal of Pure and Applied Mathematics38 (2017), 1–22.
3.
AkramM., ShahzadiS. and Borumand saeidA., Single-valued neutrosophic hypergraphs, TWMS Journal of Applied and Engineering Mathematics (2016).
4.
AkramM. and LuqmanA., Certain network models using single-valued neutrosophic directed hypergraphs, Journal of Intelligent and Fuzzy Systems (2017). DOI: 10.3233/JIFS-162347
5.
AkramM., DudekW.A. and SarwarS., Properties of bipolar fuzzy hypergraphs, Italian Journal of Pure and Applied Mathematics31 (2013), 141–160.
6.
AkramM., AlshehriN., DavvazB. and AshrafA., Bipolar fuzzy digraphs in decision support systems, J of Multi-Valued Logic and Soft Computing27 (2016), 531–551.
7.
AkramM. and ShahzadiS., Neutrosophic soft graphs with application, Journal of Intelligent & Fuzzy Systems32(1) (2017), 841–858.
8.
AkramM. and DudekW.A., Intuitionistic fuzzy hypergraphs with applications, Information Sciences218 (2013), 182–193.
9.
BergeC., Graphs and hypergraphs, North-Holland, Amsterdam Publishing Company, 1973.
10.
BhattacharyaP., Some remarks on fuzzy graphs, Pattern Recognition Letters6(5) (1987), 297–302.
11.
ChenS.M., Interval-valued fuzzy hypergraph and fuzzy partition, IEEE Transactions on Systems, Man, and Cybernetics: (Cybernetics)27(4) (1997), 725–733.
12.
DeliI., AliM. and SmarandacheF., Bipolar neutrosophic sets and their applications based on multi-criteria decision making problems, In Advanced Mechatronic Systems (ICAMechS), International Conference IEEE, 2015, pp. 249–254.
13.
Hai-LongY., Zhi-LianG., YanhongS. and XiuwuL., On single valued neutrosophic relations, Journal of Intelligent Systems32(2) (2016), 1045–1056.
14.
KaufmannA., Introduction a la Thiorie des Sous-Ensemble Flous, Masson: Paris, 1, 1977.
15.
LeeK.-M., Bipolar-valued fuzzy sets and their basic operations, Proc Int Conf, Bangkok, Thailand, 2000, pp. 307–317.
16.
LeeK.-M., Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets and bipolar-valued fuzzy sets, J Fuzzy Logic Intell Sys14(2) (2004), 125–129.
17.
Lee-KwangH. and LeeK.-M., Fuzzy hypergraph and fuzzy partition, IEEE Transactions on Systems, Man and Cybernetics25(1) (1995), 196–201.
18.
MyithiliK.K., ParvathiR. and AkramM., Certain types of intuitionistic fuzzy directed hypergraphs, Int J Mach Learn and Cyber7(2) (2016), 287–295.
19.
MajumdarP. and SamantaS.K., On similarity and entropy of neutrosophic sets, Journal of Intelligent & Fuzzy Systems26(3) (2014), 1245–1252.
20.
MordesonJ.N. and NairP.S., Fuzzy graphs and fuzzy hypergraphs, Physica Verlag, Heidelberg, Second Edition 2001, 1998.
21.
MaX., LiuQ. and ZhanJ., A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review47 (2017), 507–530.
22.
ParvathiR., ThilagavathiS. and KarunambigaiM.G., Intuitionistic fuzzy hypergraphs, Cybernetics and Information Technologies9(2) (2009), 46–53.
23.
ParvathiR., AkramM. and ThilagavathiS., Intuitionistic fuzzy shortest hyperpath in a network, Information Processing Letters113(17) (2013), 599–603.
24.
PengJ.J., WangJ.Q., ZhangH.Y. and ChenX.H., An outrankingapproach for multi-criteria decision-making problems with simplified neutrosophic sets, Applied Soft Computing25 (2014), 336–346.
25.
RosenfeldA., Fuzzy graphs, in ZadehL.A., FuK.S. and ShimuraM. (Eds), Fuzzy Sets and Their Applications, Academic Press, New York, 1975, pp. 77–95.
26.
SmarandacheF., Neutrosophy Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth, USA, 1998.
27.
SamantaS. and PalM., Bipolar fuzzy hypergraphs, International Journal of Fuzzy Logic Systems2(1) (2012), 17–28.
28.
SarwarM. and AkramM., Novel concepts of bipolar fuzzy competition graphs, Journal of Applied Mathematics and Computing54(1) (2017), 511–547.
29.
WangH., SmarandacheF., ZhangY.Q. and SunderramanR., Single valued neutrosophic sets, Multispace and Multistructure4 (2010), 410–413.
30.
YeJ., Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment, International Journal of General Systems42(4) (2013), 386–394.
31.
YeJ., Single-valued neutrosophic minimum spanning tree and its clustering method, Journal of Intelligent Systems23(3) (2014), 311–324.
32.
YeJ., Improved correlation coefficients of single-valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making, Journal of Intelligent & Fuzzy Systems27(5) (2014), 2453–2462.
33.
YeJ., A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, Journal of Intelligent & Fuzzy Systems26(5) (2014), 2459–2466.
34.
ZhangW.R., Bipolar fuzzy sets, In Fuzzy Systems Proceedings, IEEE World Congress on Computational Intelligence, 1998.
35.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
36.
ZhuK. and ZhanJ., Fuzzy parameterized fuzzy soft sets and decision making, Int J Machine Learning & Cybernetics7(6) (2016), 1207–1212.
37.
ZhanJ., LiuQ. and DavvazB., A new rough set theory: Rough soft hemirings, J Intell Fuzzy Systems28 (2015), 1687–1697.
38.
ZhanJ. and ZhuK., Reviews on decision making methods based on (fuzzy) soft sets and rough soft sets, Journal of Intelligent and Fuzzy Systems29(3) (2015), 1169–1176.
39.
ZhanJ., LiuQ. and HerawanT., A novel soft rough set: Soft rough hemirings and its multicriteria group decision making, Applied Soft Computing54 (2017), 393–402.
40.
ZhanJ. and ZhuK., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing21 (2017), 1923–1936.
41.
ZhanJ., AliM.I. and MehmoodN., On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing56 (2017), 446–457.
42.
ZhanJ., YuB. and FoteaV.-E., Characterization of two kinds of hemirings based on probability spaces, Soft Computing20 (2016), 637–648.
