Advances in Fuzzy Sets and Systems

The Advances in Fuzzy Sets and Systems publishes original research papers in the field of fuzzy sets and systems, covering topics such as artificial intelligence, robotics, decision-making, and data analysis. It also welcomes papers on variants of fuzzy sets and algorithms for computational work.

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FUZZY COMPLEMENT OF $G^c$ FOR A CONNECTED FUZZY GRAPH $G$

Authors

  • K. R. Balasubramanian
  • K. Rajeswari

Keywords:

fuzzy graphs, fuzzy complement and operations on fuzzy graphs

DOI:

https://doi.org/10.17654/0973421X22003

Abstract

In a systematic way, during the year 1975, Rosenfeld introduced fuzzy graphs. Fuzzy graphs have been introduced independently by Yeh and Bang during the same time. The main objective of this paper is to define a new concept of operation namely, fuzzy complement of a complement fuzzy graph and derive its structural properties. The graphs considered are finite, connected and simple.

Received: August 29, 2021
Revised: December 12, 2021
Accepted: January 3, 2022

References

A. Alaoui, On fuzzification of some concepts of graphs, Fuzzy Sets Systems 101 (1999), 363-389. Available: https://doi.org/10.1016/S0165-0114(97)00064-X

P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognition Letter 6 (1987), 297-302. Available: https://doi.org/10.1016/0167-8655(87)90012-2

F. Harary, Graph Theory, 3rd ed., Addison-Wesley Reading, 1972.

J. N. Mordeson and C. S. Peng, Operations on fuzzy graphs, Information Science 79 (1994), 159-170. https://doi.org/10.1016/0020-0255(94)90116-3

A. Rosenfeld, Fuzzy Sets and their Applications to Cognitive and Decision Processes, Academic Press, New York, 1975, pp. 77-95.

https://doi.org/10.1016/C2013-0-11734-5

M. S. Sunitha and A. Vijayakumar, Complement of a fuzzy graph, Indian Journal of Pure and Applied Mathematics 33 (2002), 1451-1464.

https://www.researchgate.net/publication/264994797_Complement_of_a_fuzzy_ graph

D. Venugopalam, Nagamurthi Kumar and M. Vijaya Kumar, Generalized operations on fuzzy graphs, Mathematical Theory and Modeling 3(9) (2013), 15-20.

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Published

2022-01-27

Issue

Vol. 27 No. 1 (2022)

Section

Articles

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How to Cite

FUZZY COMPLEMENT OF $G^c$ FOR A CONNECTED FUZZY GRAPH $G$. (2022). Advances in Fuzzy Sets and Systems, 27(1), 53-65. https://doi.org/10.17654/0973421X22003

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