Vol. 21 No. 3 (2022): Mapana Journal of Sciences
Research Articles

Path Induced Vertex Covering for Intuitionistic Fuzzy Graph and its Application in Disaster management

PDF
  • Josna James
Josna James
Research Scholar Mathematics, St. Thomas College, Palai

Published 2022-07-01

Keywords

  • Intuitionistic Fuzzy Graph,,
  • Intuitionistic Fuzzy Path Induced Vertex Covering,
  • covering number,,
  • Disaster management

Copyright (c) 2022

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

Graph Theory is one of the prominent tool for modelling real life problems. Due to the uncertainty
and impreciseness in such problems, Intuitionistic Fuzzy Graphs builds a conspicuous position
over graph theory and fuzzy graph theory. Now a days, conditional covering problem and set
covering problems are gaining much importance because of its increasing application. Here, we
introduced a new vertex covering to Intuitionistic Fuzzy graph, named it as Intuitionistic Fuzzy
Path Induced Vertex Covering (IFPVC). An algorithm is designed to nd the IFPVC set and IFPV
covering number for IFG. Also, an application in disaster management is provided to analyse the
plausibility of the proposed covering set.

PDF

References

  1. Atanassov Krassimir. "Intuitionistic fuzzy sets." International Journal Bioautomation 20
  2. (2016): 1
  3. Mandal, Sonia, Nupur Patra, and Madhumangal Pal. "Covering problem on fuzzy graphs and
  4. its application in disaster management system." Soft Computing 25.4 (2021): 2545-2557.
  5. Bhattacharya, Anushree, and Madhumangal Pal. "Vertex covering problems of fuzzy graphs
  6. and their application in CCTV installation." Neural Computing and Applications 33.11 (2021):
  7. -5506.
  8. Bhattacharya, Anushree, and Madhumangal Pal. "Fuzzy covering problem of fuzzy graphs
  9. and its application to investigate the Indian economy in new normal." Journal of Applied
  10. Mathematics and Computing 68.1 (2022): 479-510.
  11. Mihelic, Jurij, and Borut Robic. "Facility location and covering problems." Proc. of the 7th
  12. International Multiconference Information Society. Vol. 500. 2004.
  13. Fallah, Hamed, Ali Naimi Sadigh, and Marjan Aslanzadeh. "Covering problem." Facility Location.
  14. Physica, Heidelberg, 2009. 145-176.
  15. Akram, Muhammad, and N. O. Alshehri. "Intuitionistic fuzzy cycles and intuitionistic fuzzy
  16. trees." The Scienti c World Journal 2014 (2014).
  17. Statheropoulos, Milt, et al. "Factors that a ect rescue time in urban search and rescue (USAR)
  18. operations." Natural Hazards 75.1 (2015): 57-69.
  19. Parvathi, R., and M. G. Karunambigai. "Intuitionistic fuzzy graphs." Computational intelligence,
  20. theory and applications. Springer, Berlin, Heidelberg, 2006. 139-150.
  21. Karunambigai, M. G., R. Parvathi, and R. Buvaneswari. "Arcs in intuitionistic fuzzy graphs."
  22. Notes on Intuitionistic fuzzy sets 17.4 (2011): 37-47.
  23. Aikhuele, Daniel O., and Sarah Odo n. "A generalized triangular intuitionistic fuzzy geometric
  24. averaging operator for decision-making in engineering and management." Information 8.3
  25. (2017): 78.
  26. Wan, Shu-ping, Li-Lian Lin, and Jiu-ying Dong. "MAGDM based on triangular Atanassov's
  27. intuitionistic fuzzy information aggregation." Neural Computing and Applications 28.9 (2017):
  28. -2702.
  29. Liang, Changyong, Shuping Zhao, and Junling Zhang. "Aggregation operators on triangular
  30. intuitionistic fuzzy numbers and its application to multi-criteria decision making problems."
  31. Foundations of Computing and Decision Sciences 39.3 (2014): 189-208.
  32. Seikh, Mijanur Rahaman, Prasun Kumar Nayak, and Madhumangal Pal. "Generalized triangular
  33. fuzzy numbers in intuitionistic fuzzy environment." International journal of engineering
  34. research and development 5.1 (2012): 08-13.
  35. Gani, A. Nagoor, and M. Mohammed Jabarulla. "On searching intuitionistic fuzzy shortest
  36. path in a network." Applied Mathematical Sciences 4.69 (2010): 3447-3454.
  37. Baba, L. "Shortest path problem on intuitionistic fuzzy network." Annals of Pure and Applied
  38. Mathematics 5.1 (2013): 26-36.
  39. Li, Deng-Feng. "A ratio ranking method of triangular intuitionistic fuzzy numbers and its
  40. application to MADM problems." Computers & Mathematics with Applications 60.6 (2010):