Bipolar inverse fuzzy graphs

Document Type : Original Article

Authors

1 Department of Mathematics, Chabahar Branch, Islamic Azad University, Chabahar, Iran,

2 Department of Mathematics, Tehran Central Branch, Islamic Azad University, Tehran, Iran

Abstract

In this paper, bipolar inverse fuzzy graphs are introduced. Several operations are made on such graphs and whether these operations result in a bipolar inverse fuzzy graph is investigated. A type of bipolar inverse fuzzy graphs called strong bipolar inverse fuzzy graphs have been studied. The complement graph and dependent threshold of a bipolar inverse fuzzy graph are introduced and it is concluded that the complement of a bipolar inverse fuzzy graph is a strong bipolar inverse fuzzy graph. An inclusion condition regarding threshold graphs corresponding to two bipolar inverse fuzzy graphs with special conditions will result.

Keywords

References

[1] Akram, M. (2011). Bipolar fuzzy graphs. Information Sciences, 181, 5548-5564.
 
[2] Borzooei, R. A., Almallah, R. (2022). Inverse fuzzy multigraphs and planarity with application in decision-making. Soft Computing, 26, 1531–1539.
 
[3] Borzooei, R. A., Almallah, R., Jun, Y. B., Ghaznavi, H. (2020). Inverse Fuzzy Graphs with Applications. New Mathematics and Natural Computation, 16, 397-418.
 
[4] Kaufmann, A. (1973). Introduction a la Theorie des Sous-Ensembles Flous. Masson, Paris, 1, 41-189.
 
[5] Rosenfeld, A. (1975). Fuzzy graphs. Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, New York, 77-95.
 
[6] Samanta, S., Pal, M. (2012). Irregular Bipolar Fuzzy Graphs. Inernational Journal of Applications of Fuzzy Sets, 2, 91-102.
 
[7] Tamura, S., Higuchi, S., Tanaka, K. (1971). Pattern Classification Based on Fuzzy Relations, IEEE Trans, SMC-1, 61-66.
 
[8] Zadeh, L. A. (1971). Similarity relations and fuzzy orderings. Information Sciences, 3 (2), 177-200.
 
[9] Zhang, W. R. (1994). Bipolar fuzzy sets and relations: a computational framework forcognitive modeling and multiagent decision analysis. Proceedings of IEEE Conf, 305-309.
 
[10] Zhang, W. R. (1998). Bipolar fuzzy sets. Proceedings of FUZZ-IEEE, 835-840.
Fuzzy Systems and its Applications
Volume 6, Issue 1 - Serial Number 12
September 2023
Pages 269-285

Files

History

  • Receive Date: 12 April 2023
  • Revise Date: 02 July 2023
  • Accept Date: 02 September 2023

Share

How to cite

Statistics