Some products on interval-valued Pythagorean fuzzy graph

Downloads

DOI:

https://doi.org/10.26637/MJM0703/0033

Abstract

In this paper, the complete interval-valued Pythagorean fuzzy graphs are introduced. Direct product, strong product and semi-strong product of two interval-valued Pythagorean fuzzy graphs are defined. Also we reveal that the strong product of two complete interval-valued Pythagorean fuzzy graphs is complete. Consequently, if the direct product is strong then any one of two interval-valued Pythagorean fuzzy graphs is strong. Finally, we investigated many interesting properties on strong product and semi-strong product of two interval-valued Pythagorean fuzzy graphs.

Keywords:

Pythagorean fuzzy graph, Interval-valued Pythagorean fuzzy graph, Direct product, semi-strong product, strong product

Mathematics Subject Classification:

Mathematics
  • S.Yahya Mohamed G and Research Department of Mathematics, Government Arts College, Tiruchirappalli-620022, Tamil Nadu, India.
  • A. Mohamed Ali Department of Mathematics, G.T.N. Arts College, Dindigul-624005, Tamil Nadu, India.
  • Pages: 566-571
  • Date Published: 01-07-2019
  • Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

M. Akram and W.A.Dudek, Interval-valued fuzzy graphs, Computers and Mathematics with Applications, 61(2011) 289-299.

M. Akram, S.Naz, and B.Davvaz, Simplified intervalvalued Pythagorean fuzzy graphs with application, Complex and Intelligent Systems, 5(2019), 229-253.

K. Atanassov and G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(1989), 343349.

K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87-96.

K.T. Atanassov, Intuitionistic fuzzy sets: Theory, applications, Studies in fuzziness and soft computing, Heidelberg, New York, Physica-Verl., 1999.

A.M. Ismayil and A.M.Ali, On Strong Interval-Valued Intuitionistic Fuzzy Graphs, International Journal of Fuzzy Mathematics and Systems, 4(2)(2014), 161-168.

A.M. Ismayil and A.M Ali, On Complete Interval-valued Intuitionistic Fuzzy Graphs, Advances in Fuzzy Sets and Systems, 1(18)(2014), 71-86.

S.N. Mishra and A.Pal, Product of Interval-Valued Intuitionistic fuzzy graph, Annals of Pure and Applied Mathematics, 5(2013), 37-46.

X. Peng and Y.Yang, Fundamental properties of intervalvalued Pythagorean fuzzy aggregation operators, Int $J$ Intell Syst., 31(5)(2016), 444-487.

H. Rashmanlou and Y.B.Jun, Complete interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics, 6(3)(2013), 677-687.

A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications (L.A. Zadeh, K.S. Fu, M. Shimura, Eds.) Academic Press, New York (1975), 77-95.

S. Sahoo and M.Pal, Different types of products on intuitionistic fuzzy graphs, Pac. Sci. Rev. A., 17(3) (2015), $87-96$.

S. Yahya Mohamed and A.Mohamed Ali, Interval-valued Pythagorean fuzzy graph, Journal of Computer and Mathematical Sciences, 9(10)(2018),1497-1511.

S. Yahya Mohamed and A.Mohamed Ali, Strong Intervalvalued Pythagorean fuzzy graph, Journal of Applied Science and Computations, $5(10)(2018), 669-713$.

S. Yahya Mohamed and A.Mohamed Ali, Edge regular interval-valued Pythagorean fuzzy graph, American International Journal of Research in Science, Technology, Engineering and Mathematics, 25(1)(2019), 50-54.

S. Yahya Mohamed and A.Mohamed Ali, Modular product on intuitionistic fuzzy graphs, International Journal of Innovative Research in Science, Engineering and Technology, 6(9)(2017), 19258-19263.

S. Yahya Mohamed and A.Mohamed Ali, Max-product on intuitionistic fuzzy graph, Proceeding of $1^s t$ International Conference on Collaborative Research in Mathematical Sciences (ICCRM'S17)(2017),181-185.

RR. Yager, Pythagorean fuzzy subsets, In: Proceedings of Joint IFSA world congress and NAFIPS annual meeting, Edmonton, (2013), 57-61.

L.A. Zadeh, Fuzzy sets, Information and Control, $8(1965), 338-353$.

  • NA

Metrics

Metrics Loading ...

Published

01-07-2019

How to Cite

S.Yahya Mohamed, and A. Mohamed Ali. “Some Products on Interval-Valued Pythagorean Fuzzy Graph”. Malaya Journal of Matematik, vol. 7, no. 03, July 2019, pp. 566-71, doi:10.26637/MJM0703/0033.