Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

FUZZY SUPER SUBDIVISION MODEL WITH AN APPLICATION IN INFECTION GROWTH ANALYSIS

  • Jeba Sherlin Mohan (Department of Mathematics Loyola College University of Madras) ;
  • Samad Noeiaghdam (Industrial Mathematics Lab Irkutsk National Research Technical University) ;
  • Leo Savarimuthu (Department of Mathematics Loyola College University of Madras) ;
  • Bharathi Thangavelu (Department of Mathematics Loyola College University of Madras)
  • Received : 2023.08.23
  • Accepted : 2024.04.05
  • Published : 2024.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In our study, the integration of fuzzy graphs into classical graph theory gives rise to a novel concept known as "Fuzzy Super Subdivision." Let SSf (G) be the fuzzy super subdivision graphs, by substituting a complete bipartite graph k(2,m) (m = 1, 2, . . .) for each edge of a fuzzy graph. The attributes and properties of this newly proposed concept are briefly outlined, in addition to illustrative examples. Furthermore, significant findings are discussed on connectivity, size, degree and order of fuzzy super subdivision structures. To illustrate the practical implications of our approach, we present an application focused on analyzing the growth of infections in blood or urine samples using the Fuzzy Super Subdivision model.

Keywords

References

  1. M. Akram and B. Davvaz, Strong intuitionistic fuzzy graphs, Filomat 26 (2012), no. 1, 177-196. https://doi.org/10.2298/FIL1201177A
  2. M. Akram and W. A. Dudek, Regular bipolar fuzzy graphs, Neural. Comput. Appl. 21 (2012), 197-205.
  3. M. Akram and N. Waseem, Novel decision making method based on domination in mpolar fuzzy graphs, Commun. Korean Math. Soc. 32 (2017), no. 4, 1077-1097. https://doi.org/10.4134/CKMS.c160278
  4. M. Basher, k-Zumkeller labeling of super subdivision of some graphs, J. Egyptian Math. Soc. 29 (2021), no. 1, Paper No. 12, 16 pp. https://doi.org/10.1186/s42787-021-00121-y
  5. T. Bharathi and S. Leo, A study on Plithogenic product fuzzy graphs with application in social network, Indian J. Sci. Technol. 14 (2021), no. 40, 3051-3063.
  6. T. Bharathi, S. A. Vinoth, and S. Leo, Fuzzy radio reciprocal L-labeling on certain chemical graphs, Indian J. Sci. Technol. 14 (2021), no. 27, 2284-2292.
  7. P. Bhattacharya, Some remarks on fuzzy graphs, Pattern. Recognit. Lett. 6 (1967), no. 27, 297-302.
  8. A. Bhattacharya and M. Pal, A fuzzy graph theory approach to the facility location problem: A case study in the Indian banking system, Mathematics 11 (2023), no. 13, 2992.
  9. M. G. Coulthard, Defining urinary tract infection by bacterial colony counts: A case for 100,000 colonies/ml as the best threshold, Nephrol. 34 (2019), no. 10, 1639-1649.
  10. M. Ellouze, S. Mechti, and L. H. Belguith, A hybrid approach based on linguistic analysis and fuzzy logic to ensure the surveillance of people having paranoid personality disorder towards Covid-19 on social media, Int. J. Gen. Syst. 52 (2023), no. 3, 251-274.
  11. A. N. Gani, and S. S. Begum, Degree, order and size in intuitionistic fuzzy graphs, Int. J. Algor. Comput. Math. 3 (2010), no. 3, 11-16.
  12. A. N. Gani and J. Malarvizhi, Some aspects of total fuzzy graph, Proceedings of the International Conference on Mathematical Methods and Computation. Allied Publishers, Jamal Mohamed College. (July 24 to 25, 2009), 168-179.
  13. G. Ghorai and K. Jacob, Recent developments on the basics of fuzzy graph theory, Handbook of research on advanced applications of graph theory in modern society (2020), 419-436.
  14. M. Z. Hanif, N. Yaqoob, M. Riaz, and M. Aslam, Linear Diophantine fuzzy graphs with new decision-making approach, AIMS Math. 7 (2022), no. 8, 14532-14556. https://doi.org/10.3934/math.2022801
  15. M. Hu, Y. Zhong, S. Xie, H. Lv, and Z. Lv, Fuzzy system based medical image processing for brain disease prediction, Front Neurosc. 15 (2021), 714318.
  16. C. Kahraman, M. Deveci, E. Bolturk, and S. Turk, Fuzzy controlled humanoid robots: A literature review, Robot Auton. Syst. 134 (2020), 103643.
  17. N. Karah, R. Rafei, W. Elamin, et al, Guideline for urine culture and biochemical identification of bacterial urinary pathogens in low-resource settings, Diagnostics (Basel). 10 (2010), no. 10, 8326.
  18. A. Kauffman, Introduction a la Theorie des Sous-Emsembles Flous, Masson et Cie 1. (1973)
  19. S. Kosari, Y. Rao, H. Jiang, X. Liu, P. Wu, and Z. Shao, Vague graph structure with application in medical diagnosis, Symmetry. 12 (2020), no. 10, 1582.
  20. M. Pal, S. Sovan, and G. Ghorai, Modern trends in fuzzy, J. Graph Theor. (2020).
  21. A. Rosenfeld, Fuzzy Sets and their Applications to Cognitive and Decision Processes, Proc. U.S.-Japan Sem., Univ. Calif., Berkeley, Calif., 77-95, Academic Press, New York, 1974.
  22. S. Saravanan, V. V. Kumar, et al, Computational and mathematical methods in medicine glioma brain tumor detection and classification using convolutional neural network, Comp. Math Methods Med. (2020), 4380901.
  23. G. Sethuraman and P. Selvaraju, Decompositions of complete graphs and complete bipartite graphs into isomorphic supersubdivision graphs, Discrete Maths. 260 (2003), no. 1-3, 137-149.
  24. K. Tullus, Defining urinary tract infection by bacterial colony counts: A case for less than 100,000 colonies/mL as the threshold, Pediatr. Nephrol. 34 (2019), no. 10, 1651-1653.
  25. M. Vijaya and V. Mekala, On edge degree properties of middle, subdivision and total bipolar fuzzy graphs, Int. J. Appl. Eng. Res. 13 (2018), no. 18, 13817-13825.
  26. R. Xie, X. Li, G. Li, and R. Fu, Diagnostic value of different urine tests for urinary tract infection: A systematic review and meta-analysis, Trans.l Androl. Urol. Mar. 11 (2022), no. 3, 325-335.
  27. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
  28. Z. Zhang, J. Liu, Y. Cheng, J. Chen, H. Zhao, and X. Ren, Urine analysis has a very broad prospect in the future, Front Anal Sci. 1 (2022), 812301.