m-polar intuitionistic graphs and its properties

Subject Areas : Statistics

M. Adabitabar firozja ¹ , S. Firouzian ² , M. Taginejad ³

1 - Department of Mathematics, Qaemshar Branch, Islamic Azad University, Qaemshahr, Iran.
2 - Department of Mathematics, Payame Noor University, Tehran, Iran
3 - Department of Mathematics, Payame Noor University, Tehran, Iran

Received: 2017-05-30 Accepted : 2018-03-05 Published : 2018-01-01

Keywords: گراف, گراف فازی, مجموعه فازی شهودی, گراف فازی شهودی و مجموعه m- قط,

Abstract :

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed with fuzzy graphs or bipolar graph. With definition of fuzzy n- polar sets this problem was resolved. But all of this information is partly true and partly false. So this information can not be shown as well with n- polar fuzzy graphs. In this article introduces n-polar intuitionistic set and then we define n-polar intuitionistic graph the extension of the n- polar fuzzy graph. Also, some basic concepts such as the cartesian product, composition, union and join in the graph with proving theorems and examples are also provided.

References:

_{[1] M. Akram, N. Waseem and W. A. Dudek, Certain types of edge m-Polar fuzzy graphs, Iranian Journal of Fuzzy Systems Vol. 14, No. 4, (2017) pp. 27-50.}

 _{[2] M. Akram, B. Davvaz, Strong intuitionistic fuzzy graphs, Filomat 26 (1) (2012) 177-195.}

 [3] M. Akram, Bipolar fuzzy graphs, Information Sciences 181 (2011) 5548–5564.

 [4] K.T. Atanassove, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986) 87-96.

 [5] J. Chen, S. Li, S. Ma, X. Wang, m-Polar fuzzy sets: an extension of bipolar fuzzy sets. Hindwai Publishing Corporation, Sci. World J. (2014) 8. Article   Id: 416530,http://dx.doi.org/10.1155/2014/416530.

 [6] G. Ghorai, M. Pal, Some properties of m-polar fuzzy graphs, Pacific Science Review A: Natural Science and Engineering 18 (2016) 38-46.

 [7] G. Ghorai, M. Pal, A study on m-polar fuzzy planar graphs, Int. J. Comput. Sci. Math. 7 (3) (2016) 283-292.

 [8] H. Rashmanlou, R.A. Borzooei, S. Samanta, M. Pal, Properties of interval valued intuitionistic (S,T) - Fuzzy graphs, Pacific Science Review A: Natural Science and Engineering 18 (2016) 30-37.

  [9] A. Kauffman, Introduction a la theorie des sous-emsembles 503 ous, Masson et Cie 1, 1973.

 [10] L.A. Zadeh, Similarity relations and fuzzy ordering, Inf. Sci. 3 (1971) 177-200.

 [11] L.A. Zadeh, Fuzzy sets, Inf. Control  (1965) 338-353.

[12] W.R. Zhang, Bipolar fuzzy sets, in: Proceedings of Fuzzy-IEEE, 1998, pp. 835-840.