PRODUCT OF BIPOLAR INTUITIONISTIC FUZZY GRAPHS AND THEIR DEGREE
In this paper, bipolar intuitionistic fuzzy graphs with four operations namely Cartesian product, composition, tensor product, normal product are dened. Also, the degrees of the vertices of the resultant graphs which are obtained from two given bipolar intuitionistic fuzzy graphs G1 and G2 using the operations Cartesian product, composi- tion, tensor product, normal product are determined.
___
- [1] Atanassov K.T., (1999). Intuitionistic fuzzy sets. Theory and Applications, studies in fuzziness and soft Computing, physica-verl., Heidelberg, New York
- [2] Akram M., (2011). Bipolar fuzzy graphs. Information Sciences 181: 5548–5564.
- [3] Akram M. and Davvaz B., (2012). Strong intuitionistic fuzzy graphs. Filomat 26(1): 177–196.
- [4] Al-Shehrie N. O., Akram M., (2015). Bipolar fuzzy competition graphs. Ars Combinatoria 121: 385– 402.
- [5] Atanassov K. T., (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20: 87–96.
- [6] Hai-Long Yang et al.(2013). Notes on “Bipolar fuzzy graphs”. Information Sciences 242: 113–121.
- [7] Mordeson J. N., Nair P. S., (2001). Fuzzy Graphs and Fuzzy Hypergraphs. Heidelberg: Physical Verlage.
- [8] Mordeson J.N., Peng C. S., (1994). Operation on fuzzy graphs. Information Sciences 79: 159–170.
- [9] Nagoorgani A., Radha K., (2009). The degree of vertex in some fuzzy graphs. International Journal of Algorithms, Computing and Mathematics 2: 107—116.
- [10] Pal M., Samanta S., Rashmanlou H., (2015). Some results on interval-valued fuzzy graphs. International Journal of Computer Science and Electronics Engineering 3 (3): 205–211.
- [11] Pramanik T., Samanta S., Pal M., (2014). Interval-valued fuzzy planar graphs. International Journal of Machine Learning and Cybernetics 7 (4): 653–664.
- [12] Rashmanlou H., Pal M., (2013). Balanced interval-valued fuzzy graphs. Journal of Physical Sciences 17: 43–57.
- [13] Rashmanlou H., Pal M., (2013). Some properties of highly irregular interval valued fuzzy graphs. World Applied Sciences Journal 27 (12): 1756–1773.
- [14] Rashmanlou H., Samanta S., Pal M., Borzooei R., A., (2015). A study on bipolar fuzzy graphs. Journal of Intelligent and Fuzzy Systems 28: 571–580.
- [15] Rashmanlou H., Samanta S., Pal M., Borzooei R., A., (2015) Bipolar fuzzy graphs with categorical properties. The International Journal of Computational Intelligence Systems 8 (5): 808–818.
- [16] Rosenfield A., (1975). Fuzzy graphs. Fuzzy Sets and Their Application (L. A. Zadeh, K. S. Fu, M. Shimura, Eds.) Academic press, New York: 77–95.
- [17] Rashmanlou H., Samanta S., Borzooei R. A., Pal M., (2014). A study on bipolar fuzzy graphs. Journal of Intelligent and Fuzzy Systems 28: 571-–580.
- [18] Sahoo S., Pal M., (2015). Different types of products on intuitionistic fuzzy graphs. Pacific Science Review A: Natural Science and Engineering 17(3): 87–96.
- [19] Sahoo S., Pal M., (2015). Intuitionistic fuzzy competition graph. Journal of Applied Mathematics and Computing 52(1): 37–57.
- [20] Sahoo S., Pal M., (2016). Intuitionistic fuzzy tolerance graphs with application. Journal of Applied Mathematics and Computing DOI:10.1007/s12190-016-1047-2.
- [21] Sahoo S., Pal M., (2016). Product of intuitionistic fuzzy graphs and degree. Journal of Intelligent and Fuzzy Systems 32(1): 1059-1067.
- [22] Samanta S, Pal A., Pal M., (2014). New concepts of fuzzy planar graphs. International Journal of Advanced Research in Artificial Intelligence 3 (1): 52–59.
- [23] Samanta S., Pal M., (2011). Fuzzy threshold graphs. CIIT International Journal of Fuzzy Systems 3: 360–364.
- [24] Samanta S., Pal M., (2011). Fuzzy tolerance graphs. International Journal of Latest Trends in Mathematics 1: 57–67.
- [25] Samanta S., Pal M., (2012). Irregular bipolar fuzzy graphs. International Journal of Applications of Fuzzy Sets 2: 91–102.
- [26] Samanta S., Pal M., (2013). Fuzzy k-competition graphs and p-competition fuzzy graphs. Fuzzy Information and Engineering 5: 191–204.
- [27] Samanta S., Pal M., (2013). Telecommunication System Based on Fuzzy Graphs. J. Telecommun. Syst. Manage. 3: 1–6.
- [28] Samanta S., Pal M., (2014). Some more results on bipolar fuzzy sets and bipolar fuzzy intersection graphs. The Journal of Fuzzy Mathematics 22(2): 253–262.
- [29] Samanta S., Pal M., (2015). Fuzzy planar graph. IEEE Transaction on Fuzzy Systems, 23 (6): 1936– 1942
- [30] Zadeh L., A., (1965). Fuzzy set. Information and Control 8: 338-353.
- [31] Zhang W., R., (1994). Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. Proceedings of IEEE Conf (1994): 305–309.