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Isomorphic Property and Some Operations of Picture Fuzzy Graphs
Volume 1, Issue 1, December 2020, Pages: 22-29
Received: Nov. 10, 2020; Accepted: Dec. 2, 2020; Published: Dec. 22, 2020
Authors
Yashwant Das Vaishnaw, Department of Mathematics, Maharshi Vedvyas Government Post Graduate College, Bhakhara, Pandit, Ravishankar Shukla University, Raipur (Chhattisgarh), India
Kajal Kiran Gulhare, Department of Computer Science, Government Edpuganti Raghavendra Rao Post, Graduate Science College, Atal Bihari Vajpayee University, Bilaspur (Chhattisgarh), India
Dildar Tandon, Department of Mathematics, Doctor Jwala Prasad, Mishra Government Post Graduate Science College Mungeli, Atal Bihari Vajpayee University, Bilaspur (Chhattisgarh), India
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Abstract
In this paper picture fuzzy graph has shown more advantage in handling vagueness and uncertainty than fuzzy set. We have applied concept of picture fuzzy set to fuzzy set. Picture fuzzy graph is generalization of fuzzy graph. The concept of picture fuzzy graph has discussed here. In this paper complement and Ring sum operation of picture fuzzy graphs has discussed isomorphic property of picture fuzzy graphs. We have used picture Fuzzy graph play important role in representation of many uncertain decision making problem in daily life since Picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, e.g. number theory, coding theory, cryptography, computer science, operation research, also we are using certain concepts of bipolar fuzzy directed hypergraphs Finally we have proved the Ring sum of two picture fuzzy graphs is also a picture fuzzy graph.
Keywords
Fuzzy Graph, Isomorphism, Picture Fuzzy Graph, Complement of Fuzzy Graph
Yashwant Das Vaishnaw, Kajal Kiran Gulhare, Dildar Tandon, Isomorphic Property and Some Operations of Picture Fuzzy Graphs, Advances. Vol. 1, No. 1, 2020, pp. 22-29. doi: 10.11648/j.advances.20200101.14
References
[1]
Akram, M.; Luqman, A. Certain concepts of bipolar fuzzy directed hypergraphs. Mathematics 2017, 5, 17.
[2]
A. Nagoor Gani and J. Malarvizhi “Isomorphism on Fuzzy Graphs” International Journal of Computational and Mathematical Sciences 2: 42008.
[3]
A. Rosenfeld and fuzzy graphs. In Fuzzy Sets and their applicationsto Congnitive and Dicision processes. Zadeh L. A., Fu K. S. Shimura M., Eds. Acdemic Press. New York, 1975, 77-95.
[4]
Cen Zuo, Anita Pal and Arindam Day “New Concepts of Fuzzy Graphswith plication” Mathematics 2019 (MDPI), 24 May 2019, doi: 10.3390/maths7050470.
[5]
Johan N. Mordeson and Chang-Shyh Peng, operations on fuzzy graph, Information science 79, 159-170 (1994).
[6]
J. N. Mordeson P. S. Nair, Fuzzy Graphs and Fuzzy Hyper graphs, physica-Verlag, Heidelberg, 2000.
[7]
L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965) 338-353.
[8]
M. S. Sunitha andA. VijayaKumar, Complement of fuzzy graph Indian J. pureappl. Math. 33 (9), 1451-1464, 2002.
[9]
[10]
M. Akramand R. Akmal, Intuitionistic Fuzzy Graph Structures, Kragujevac Journal of Mathematics Volume 41 (2) (2017), Pages 219–237.
[11]
R. T. Yeh and S. Y. Banh. Fuzzy relations, fuzzy graphs and their applicationsto clustering analysis. In fuzzy sets and their applications to Cognitive and Decision Processes Zadeh. L. A. Fu K. S., Shimara, M. Eds Academic Press, New York (1975).
[12]
S. Samanta and B. Sarkar “Representation of completions by generalized fuzzy graphs”International Journal of computational Intelligence system vol. 11 (2018) 1005-1015.
[13]
Sarwar, M.; Akram, M.; Alshehri, N. O. A new method to decision-making with fuzzy competition hypergraphs. Symmetry 2018, 10, 404.
[14]
Sing P. Correlation coefficients for Picture fuzzy set J. Intel. Fuzzy Syst. 2015, 28, 591-604.
[15]
Y. Vaishnaw and A. S. Ranadive “On isomorphism between fuzzy graphs” Chhattisgarh Journal of science and technology, volume 3 & 4 (2007).
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