پیوندهای مفید
آمار
| تعداد نشریات | 31 |
| تعداد شمارهها | 443 |
| تعداد مقالات | 3,920 |
| تعداد مشاهده مقاله | 6,597,381 |
| تعداد دریافت فایل اصل مقاله | 4,400,505 |
Finding a generalized positive solution equation for a trapezoidal fully fuzzy sylvester matrix | ||
| Journal of Hyperstructures | ||
| دوره 14، شماره 2، اسفند 2025، صفحه 167-175 اصل مقاله (1.56 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2024.15376.1024 | ||
| نویسنده | ||
| Ram Milan Singh* | ||
| Institute for Excellence in Higher Education, Bhopal, India | ||
| چکیده | ||
| The solvability of Sylvester matrix equations is relevant to many issues in control theory and systems theory. Fuzzy numbers should be used to represent at least some of the system’s parameters in many applications instead of crisp ones. The solutions to the fuzzy Sylvester matrix problem are only given with triangular fuzzy numbers in the majority of the earlier literature. Two analytical approaches to the solution of the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation are presented in this study. The Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation is transformed utilising the current arithmetic fuzzy multiplication operations into an analogous system of crisp Sylvester Matrix Equations. We look into the uniqueness and necessary and sufficient circumstances for the existence of the positive fuzzy solutions to the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation. We look into the uniqueness and necessary and sufficient circumstances for the existence of the positive fuzzy solutions to the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation. Furthermore, the equivalency between the Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation and the solution to the Sylvester Matrix Equation system is examined. One example problem is solved to demonstrate the suggested methods. | ||
| کلیدواژهها | ||
| Schur decomposition؛ trapezoidal fuzzy numbers؛ Kronecker product؛ totally fuzzy Sylvester matrix equations؛ and Bartels Stewart | ||
| مراجع | ||
|
[1] L. Syrmos and F. L. Lewis, Coupled and constrained Sylvester equations in system design, Circuits Syst Signal Process, 13 (1994), 663-694. [2] L. Chen and P. Wang, Fuzzy relation equations (I): the general and specialized solving algorithms, Soft Comput Fusion Found Methodol Appl., 6 (2002), 428-435. [3] M. Sanches, J. Nascimento, and J. Marques, Medical image noise reduction using the Sylvester-Lyapunov equation, IEEE Trans Image Process, 17 (2008), 1522-1539. [4] D. Calvetti and L. Reichel, Application of ADI iterative methods to the restoration of noisy images, SIAM J Matrix Anal Appl, 17 (1996), 165-186. [5] A. Bouhamidi and K. Jbilou, Tikhonov-regularization methods in image restoration, J Comput Appl Math, 206 (2007), 86-98. [6] Q. He, L. Hou, and J. Zhou, The solution of fuzzy Sylvester matrix equation, Soft Comput, 22 (2018), 6515-6523. [7] S. Rao and J. P. Sawyer, Fuzzy nite element approach for analysis of imprecisely de ned systems, AIAA J, 33 (1995), 2364-2370. [8] M. Dehghan, B. Hashemi, and M. Ghatee, Computational methods for solving fully fuzzy linear systems, Appl Math Comput, 179 (2006), 328-343. [9] X. Guo, Approximate solution of fuzzy Sylvester matrix equations, Proceedings of the 2011 7th International Conference on Computational Intelligence and Security (CIS 2011), 2011, 52-56. [10] M. Keyanpour, D. K. Salkuyeh, and H. Moosaei, On the solution of the fully fuzzy Sylvester matrix equation, Int J Model Simul, 40 (2020), 80-85. [11] D. Dubois and H. Prade, Operations on fuzzy numbers, Int J Syst Sci, 9 (1978), 613-626. [12] X. Guo and D. Shang, Fuzzy approximate solution of positive fully fuzzy linear matrix equations, J Appl Math, vol. 2013, Article ID 178209. [13] G. Malkawi, N. Ahmad, and H. Ibrahim, Solving the fully fuzzy Sylvester matrix equation with triangular fuzzy number, Far East J Math Sci, 98 (2015), 37-55. [14] S. Daud, N. Ahmad, and G. Malkawi, Positive solution of pair fully fuzzy matrix equations, Malaysian J Math Sci, 12 (2018), 383-400. [15] L. Hou, J. Zhou, and Q. He, An extension method for fully fuzzy Sylvester matrix equation, Soft Comput, 25 (2021), 5763-5774. [16] A. Elsayed, N. Ahmad, and G. Malkawi, On the solution of fully fuzzy Sylvester matrix equation with trapezoidal fuzzy numbers, Comput Appl Math, 39 (2020), Article ID 278. [17] H. Henderson and S. Searle, The vec-permutation matrix, the vec operator and Kronecker products: a review, Linear Multilinear Algebra, 9 (1981), 271-288. [18] A. Graham, Kronecker Products and Matrix Calculus with Applications, Courier Dover Publications, 2018. [19] C. Paige and C. Van Loan, A Schur decomposition for Hamiltonian matrices, Linear Algebra Appl, 41 (1981), 11-32. [20] H. Wang and L. Chen, Symmetric positive solutions to triangular fuzzy Sylvester equations. International Journal of Fuzzy Systems, 20(2) (2022), 311-xxx | ||
|
آمار تعداد مشاهده مقاله: 154 تعداد دریافت فایل اصل مقاله: 130 |
||