Intuitionistic fuzzy signed graphs of the second type ∗

Seema Mehra; Manjeet  Singh

doi:10.48165/

Authors

Seema Mehra Department of Mathematics, M.D. University, Rohtak, Haryana, India.
Manjeet Singh Department of Mathematics, Government College, Bawal, Rewari, Haryana, India.

DOI:

https://doi.org/10.48165/

Keywords:

Intuitionistic Fuzzy Graph, Intuitionistic fuzzy graphs of second type, Intuitionistic fuzzy signed graphs of second type, Balanced Intuitionistic fuzzy signed graphs of second type

Abstract

The aim of this paper is to introduce a new concept of intuitionistic fuzzy signed graph of second type as an extension of the intuitionistic fuzzy graph of second type defined by Sheik and Srinivasan (Sheik Dhavudh, S. and Srinivasan, R. (2017), In tuitionistic fuzzy graphs of second type, Advances in Fuzzy Mathematics, 12, 197–204; Sheik Dhavudh, S. and Srinivasan, R. (2017), A study on intuitionistic fuzzy graphs of second type, International Journal of Mathematical Archive, 8(8), 31–33; Sheik Dhavudh, S. and Srinivasan, R. (2017), Properties of intuitionistic fuzzy graphs of second type, In ternational Journal of Computational and Applied Mathematics, 12(3), 815–823) and the intuitionistic fuzzy signed graph defined by Mishra and Pal (Mishra, S.N. and Pal, A. (2016), Intuitionistic fuzzy signed graphs, International Journal of Pure and Applied Mathematics,106 (6), 113–122). Also we establish some of its properties.

References

Akram, M. and Akmal, R. (2016). Operations on intuitionistic fuzzy graph structures, Fuzzy Information and Engineering, 8(4), 389–410.

Atanassov, K.T. (1999). Intuitionistic Fuzzy Sets, Springer Physica - Verlag, Berlin. [3] Bhattacharya, P. (1987). Some remarks on fuzzy graphs, Pattern Recognition Letters, 6, 297–302. [4] Cartwright, D. and Harary, F. (1956). Structural balance: a generalization of Heider’s theory, Psych. Rev., 63, 277–293.

Gani, N. and Begum, S.S (2010). Degree, order and size in intuitionistic fuzzy graphs, International Journal of Algorithms, Computing and Mathematics, 3(3), 11–16.

Harary, F. (1953). On the notion of balance of a signed graph, Michigan Math. J., 2(2), 143–146. [7] Karunambigai, M.G. and Parvathi, P. (2006). Intuitionistic fuzzy graphs, Proceedings of 9th Fuzzy Days International Conference on Computational Intelligence, Advances in Soft Computing: Com

putational Intelligence, Theory and Applications, Springer-Verlag, 20, 139—150. [8] Mishra, S.N. and Pal, A. (2016). Intuitionistic fuzzy signed graphs, International Journal of Pure and Applied Mathematics, 106 (6), 113–122.

Nirmala, G. and Prabavathi, S. (2015). Mathematical models in terms of balanced signed fuzzy graphs with generalized modus ponens, International Journal of Science and Research, 4(7), 2415– 2419.

Parvathi, R. and Palaniappan, N. (2004). Some operations on intuitionistic fuzzy set of second type, Notes on Intuitionistic Fuzzy Sets, 10(2), 1–19.

Parvathi, R., Karunambigai, M.G. and Atanassov, K.T. (2009). Operations on intuitionistic fuzzy graphs, Fuzzy Systems, 2009, FUZZY-IEEE 2009, IEEE International Conference, 1396–1401. [12] Sheik Dhavudh, S. and Srinivasan, R.: (2017). Intuitionistic fuzzy graphs of second type, Advances in Fuzzy Mathematics, 12, 197–204.

Sheik Dhavudh, S. and Srinivasan, R. (2017). A study on intuitionistic fuzzy graphs of second type, International Journal of Mathematical Archive, 8(8), 31–33.

Sheik Dhavudh, S. and Srinivasan, R. (2017). Properties of intuitionistic fuzzy graphs of second type, International Journal of Computational and Applied Mathematics, 12(3), 815–823. [15] Zadeh, L.A. (1965). Fuzzy sets, Information and Control, 8, 338-353.

Zaslavsky, T. (1982). Signed graphs, Discrete Applied Mathematics, 4, 47–74.