Complex Fuzzy Dynamical Graphs and their Applications in Signals Processing

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-23-2025-9
Published: Jan 14, 2025
Cite as:
Saima Anis, Madad Khan, Muhammad Mazhar, Muhammad Naveed, Kostaq Hila, Complex Fuzzy Dynamical Graphs and their Applications in Signals Processing, Int. J. Anal. Appl., 23 (2025), 9.

Main Article Content

Saima Anis, Madad Khan, Muhammad Mazhar, Muhammad Naveed, Kostaq Hila

Abstract

In this paper we introduce the concepts of complex fuzzy dynamic graphs, complex fuzzy diagonal matrices and complex fuzzy Laplacian matrices. We use these graphs and their laplacian matrices as mathematical framework for applications in Sciences, especially signals processing. We define absolute average eigenvalues of the Complex Laplacian matrices and explore the properties of these matrices with their eigenvalues. We develop an algorithm using the absolute eigenvalues of the Laplacian matrices and apply this algorithm to signal and systems. Our study begins by establishing the theoretical foundation of complex fuzzy dynamic graphs, highlighting their role to model within dynamic systems including two dimensional uncertainties. We investigates the complex fuzzy Laplacian matrices obtain from these graphs. Our main focus is on the absolute eigenvalues of these matrices, which hold a vital role into the graph’s structural characteristics and behavior. In the context of signals processing, the research demonstrates how these absolute eigenvalues serve as essential matrices for system characterization. This study presents novel methods to analyze signals on complex fuzzy dynamic graphs. These methods are particularly relevant in scenarios where signals are influenced by dynamic and uncertain environments.

Article Details

References

  1. A.S. Alkouri, A.R. Salleh, Complex Intuitionistic Fuzzy Sets, in: Kuala Lumpur Convention Centre, Kuala Lumpur, Malaysia, 2012: pp. 464–470. https://doi.org/10.1063/1.4757515.
  2. H. Garg, D. Rani, Complex Interval-Valued Intuitionistic Fuzzy Sets and Their Aggregation Operators, Fundam. Inform. 164 (2019), 61–101. https://doi.org/10.3233/FI-2019-1755.
  3. H. Garg, D. Rani, Some Results on Information Measures for Complex Intuitionistic Fuzzy Sets, Int. J. Intell. Syst. 34 (2019), 2319–2363. https://doi.org/10.1002/int.22127.
  4. H. Garg, D. Rani, A Robust Correlation Coefficient Measure of Complex Intuitionistic Fuzzy Sets and Their Applications in Decision-Making, Appl. Intell. 49 (2019), 496–512. https://doi.org/10.1007/s10489-018-1290-3.
  5. D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex Fuzzy Sets, IEEE Trans. Fuzzy Syst. 10 (2002), 171–186. https://doi.org/10.1109/91.995119.
  6. D. Rani, H. Garg, Complex Intuitionistic Fuzzy Power Aggregation Operators and Their Applications in Multicriteria Decision-Making, Expert Syst. 35 (2018), e12325. https://doi.org/10.1111/exsy.12325.
  7. K. Ullah, T. Mahmood, Z. Ali, N. Jan, On Some Distance Measures of Complex Pythagorean Fuzzy Sets and Their Applications in Pattern Recognition, Complex Intell. Syst. 6 (2020), 15–27. https://doi.org/10.1007/s40747-019-0103-6.
  8. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.
  9. Z. Shao, S. Kosari, H. Rashmanlou, M. Shoaib, New Concepts in Intuitionistic Fuzzy Graph with Application in Water Supplier Systems, Mathematics 8 (2020), 1241. https://doi.org/10.3390/math8081241.
  10. H. Rashmanlou, S. Samanta, M. Pal, R.A. Borzooei, Product of Bipolar Fuzzy Graphs and Their Degree, Int. J. Gen. Syst. 45 (2016), 1–14. https://doi.org/10.1080/03081079.2015.1072521.
  11. H. Rashmanlou, S. Samanta, M. Pal, R.A. Borzooei, A Study on Bipolar Fuzzy Graphs, J. Intell. Fuzzy Syst. 28 (2015), 571–580. https://doi.org/10.3233/IFS-141333.
  12. H. Rashmanlou, M. Pal, Some Properties of Highly Irregular Interval-Valued Fuzzy Graphs, World Appl. Sci. J. 27 (2013), 1756–1773.
  13. S. Zeng, M. Shoaib, S. Ali, F. Smarandache, H. Rashmanlou, F. Mofidnakhaei, Certain Properties of Single-Valued Neutrosophic Graph With Application in Food and Agriculture Organization, Int. J. Comput. Intell. Syst. 14 (2021), 1516–1540. https://doi.org/10.2991/ijcis.d.210413.001.
  14. Z. Shao, S. Kosari, M. Shoaib, H. Rashmanlou, Certain Concepts of Vague Graphs With Applications to Medical Diagnosis, Front. Phys. 8 (2020), 357. https://doi.org/10.3389/fphy.2020.00357.
  15. J.J. Buckley, Fuzzy Complex Numbers, Fuzzy Sets Syst. 33 (1989), 333–345. https://doi.org/10.1016/0165-0114(89)90122-X.
  16. N. Yaqoob, M. Akram, Complex Neutrosophic Graph, Bull. Comput. Appl. Math. 6 (2018), 2224–8659.
  17. M. Shoaib, S. Kosari, H. Rashmanlou, M.A. Malik, Y. Rao, Y. Talebi, F. Mofidnakhaei, Notion of Complex Pythagorean Fuzzy Graph With Properties and Application, J. Multi-Valued Logic Soft Comput. 34 (2020), 553–586.
  18. M. Shoaib, W. Mahmood, Q. Xin, F. Tchier, Certain Operations on Picture Fuzzy Graph with Application, Symmetry 13 (2021), 2400. https://doi.org/10.3390/sym13122400.