S. NAZ, S. ASHRAF, H. RASHMANLOU

1616

MEASUREMENT OF PLANARITY IN PRODUCT BIPOLAR FUZZY GRAPHS

Bipolar fuzzy set theory provides a basis for bipolar cognitive modeling and multiagent decision analysis, where in some situations, the product operator may be preferred to the min operator, from theoretical and experimental aspects. In this paper, the denition of product bipolar fuzzy graphs PBFGs in [16] is modied. The concepts of product bipolar fuzzy multigraphs PBFMGs , product bipolar fuzzy planar graphs PBFPGs and product bipolar fuzzy dual graphs PBFDGs are introduced and their properties are investigated. Meanwhile, the product bipolar fuzzy planarity value of PBFPG is introduced. The relation between PBFPG and PBFDG is also established. Finally, an application of the proposed concepts is provided.
Keywords:

Product bipolar fuzzy graph product bipolar fuzzy multigraph, product bipolar fuzzy planar graph, product bipolar fuzzy dual graph.,

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  • [1] Akram, M., (2011), Bipolar fuzzy graphs, Information Sciences, 181(24), pp. 5548-5564.
  • [2] Akram, M. and Dudek, W. A., (2012), Regular bipolar fuzzy graphs, Neural Computing and Applications, 21(1), pp. 197-205.
  • [3] Akram, M., (2013), Bipolar fuzzy graphs with applications, Knowledge-Based Systems, 39, pp. 1-8.
  • [4] Akram, M., Samanta, S. and Pal, M., (2017), Application of bipolar fuzzy sets in planar graphs, International Journal of Applied and Computational Mathematics, 3(2), pp. 773-785.
  • [5] Alshehri, N. and Akram, M., (2014), Intuitionistic fuzzy planar graphs, Discrete Dynamics in Nature and Society, pp. 1-9.
  • [6] Ashraf, S., Naz, S. and Kerre, E. E., (2018), Dombi fuzzy graphs, Fuzzy Information and Engineering, 10(1), pp. 58-79.
  • [7] Ashraf, S., Naz, S., Rashmanlou, H. and Malik, M. A., (2017), Regularity of graphs in single-valued neutrosophic environment, Journal of Intelligent & Fuzzy Systems, 33(1), pp. 529-542.
  • [8] Ghorai, G. and Pal, M., (2017), Certain types of product bipolar fuzzy graphs, International Journal of Applied and Computational Mathematics, 3(2), pp. 605-619.
  • [9] Jabbar, N. A., Naoom, J. H. and Ouda, E. H., (2009), Fuzzy dual graph, J Al-Nahrain Univ, 12(4), pp. 168-171.
  • [10] Lee, K. M., (2000), Bipolar-valued fuzzy sets and their basic operations, In Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, pp. 307-312.
  • [11] Naz, S., Ashraf, S. and Karaaslan, F., (2018), Energy of a bipolar fuzzy graph and its application in decision making, Italian Journal of Pure and Applied Mathematics, 40, pp. 339-352.
  • [12] Naz, S., and Malik, M. A., (2018), Single valued neutrosophic line graphs, TWMS Journal of Applied and Engineering Mathematics, 8(2), pp. 483-494.
  • [13] Naz, S., Rashmanlou, H. and Malik, M. A., (2017), Operations on single-valued neutrosophic graphs with application, Journal of Intelligent & Fuzzy Systems, 32(3), pp. 2137-2151.
  • [14] Naz, S., Malik, M. A. and Rashmanlou, H., (2018), Hypergraphs and transversals of hypergraphs in interval-valued intuitionistic fuzzy setting, The Journal of Multiple-Valued Logic and Soft Computing, 30 (4-6), pp. 399-417.
  • [15] Pal, A., Samanta, S. and Pal, M., (2013), Concept of fuzzy planar graphs, In Science and Information Conference (SAI) IEEE, pp. 557-563.
  • [16] Rashmanlou, H., Samanta, S., Pal, M. and Borzooei, R. A., (2015), A study on bipolar fuzzy graphs, Journal of Intelligent & Fuzzy Systems, 28(2), pp. 571-580.
  • [17] Rosenfeld, A., (1975), Fuzzy graphs, Fuzzy Sets and their Applications (L. A. Zadeh, K. S. Fu, M. Shimura, Eds.) Academic Press, New York, pp. 77-95.
  • [18] Samanta, S., Pal, M. and Pal, A., (2014), New concepts of fuzzy planar graph, International Journal of Advanced Research in Artificial Intelligence, 3(1), pp. 52-59.
  • [19] Yager, R. R., (1986), On the theory of bags, International Journal of General System, 13(1), pp. 23-37.
  • [20] Zadeh, L. A., (1965), Fuzzy sets, Information and Control, 8(3), pp. 338-353.
  • [21] Zhang, W-R., (1994), Bipolar fuzzy sets and relations: a computational framework forcognitive modeling and multiagent decision analysis, Proceedings of IEEE conference, pp. 305-309.
  • [22] Zhang, W-R., (1998), Bipolar fuzzy sets, Proceedings of FUZZ-IEEE, pp. 835-840.
TWMS Journal of Applied and Engineering Mathematics-Cover
  • ISSN: 2146-1147
  • Başlangıç: 2010
  • Yayıncı: Turkic World Mathematical Society
Arşiv
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