پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 31 |
| تعداد شمارهها | 863 |
| تعداد مقالات | 8,327 |
| تعداد مشاهده مقاله | 16,755,893 |
| تعداد دریافت فایل اصل مقاله | 11,191,425 |
Uncertainty propagation in linear fuzzy difference equations via Hamacher t-norms | ||
| Iranian Journal of Fuzzy Systems | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 شهریور 1405 اصل مقاله (540.32 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.53468.9464 | ||
| نویسندگان | ||
| Vinicius F. Wasques* 1؛ Jefferson David Alves2 | ||
| 1Ilum School of Science, Brazilian Center for Research in Energy and Materials, Campinas, Brazil | ||
| 2São Paulo State University, Rio Claro, Brazil | ||
| چکیده | ||
| This paper investigates linear fuzzy difference equations whose initial conditions are represented by fuzzy numbers. The classical arithmetic operations involved in recurrence relations are extended to the fuzzy $t$-norm-based extension principles, allowing the incorporation of interactivity between fuzzy variables. In particular, this paper deals with Hamacher $t$-norm, which provides a flexible interaction mechanism between different dependence regimes. The paper focuses on the dynamical behavior and uncertainty propagation of fuzzy sequences generated by interactive arithmetic. Moreover, theoretical results concerning the modal dynamics, support evolution, spectral stability, and sensitivity with respect to the interaction parameter are established. Computational aspects of the proposed algorithms are also discussed, including their asymptotic complexity. To illustrate the proposed framework, classical discrete dynamical systems, including fuzzy Fibonacci recurrences and simple population growth models, are analyzed under uncertain initial conditions. A comparative study between the Hamacher interaction and Zadeh’s extension principle is presented, highlighting how different interaction mechanisms influence the propagation and concentration of uncertainty in fuzzy difference equations. | ||
| کلیدواژهها | ||
| Fuzzy Difference Equation؛ Biomathematics؛ Fuzzy Interactivity؛ Hamacher t-norm | ||
| مراجع | ||
|
[1] R. Al-Hmouz, W. Pedrycz, A. Ammari, A. Al-Hmouz, Fuzzy relational models: Convolution techniques and optimization, Journal of Intelligent and Fuzzy Systems, 50(4) (2026), 1234-1255. https://doi.org/10.1177/ 18758967251371265
[2] L. C. Barros, R. C. Bassanezi, W. A. Lodwick, A first course in fuzzy logic, fuzzy dynamical systems, and biomath ematics, Springer-Verlag Berlin Heidelberg, 2017. https://doi.org/10.1007/978-3-031-50492-1
[3] L. C. Barros, F. Santo Pedro, Fuzzy differential equations with interactive derivative, Fuzzy Sets and Systems, 309 (2017), 64-80. https://doi.org/10.1016/j.fss.2016.04.002
[4] E. Bartl, G. J. Klir, Fuzzy relational equations in general framework, International Journal of General Systems, 43(1) (2014), 1-18. https://doi.org/10.1080/03081079.2013.850197
[5] L. Edelstein-Keshet, Mathematical models in biology, Random House, 1988. https://doi.org/10.1137/1. 9780898719147
[6] S. N. Elaydi, An introduction to difference equations, 3rd ed., Springer, 2005. https://doi.org/10.1007/ 0-387-27602-5
[7] E. Esmi, L. C. de Barros, V. F. Wasques, Some notes on the addition of interactive fuzzy numbers, in: R. Kearfott, I. Batyrshin, M. Reformat, M. Ceberio, V. Kreinovich (eds.), Fuzzy Techniques: Theory and Ap plications, IFSA/NAFIPS 2019, Advances in Intelligent Systems and Computing, 1000, Springer, Cham, 2019. https://doi.org/10.1007/978-3-030-21920-8_23
[8] E. Esmi, V. F. Wasques, L. C. Barros, Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions, Fuzzy Sets and Systems, 424 (2021), 105-131. https://doi.org/10.1016/j.fss.2021. 03.005
[9] R. Fullér, P. Majlender, On interactive fuzzy numbers, Fuzzy Sets and Systems, 143(3) (2004), 355-369. https: //doi.org/10.1016/S0165-0114(03)00180-5
[10] S. Goldberg, Introduction to difference equations with illustrative examples from economics, psychology and sociology, Dover Publications, Inc., New York, 1986.
[11] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Springer, Dordrecht, 2000. https://doi.org/10.1007/ 978-94-015-9540-7
[12] P. Li, S. C. Fang, A survey on fuzzy relational equations, part I: Classification and solvability, Fuzzy Optimization and Decision Making, 8 (2009), 179-229. https://doi.org/10.1007/s10700-009-9059-0
[13] P. Li, S. C. Fang, On the unique solvability of fuzzy relational equations, Fuzzy Optimization and Decision Making, 10 (2011), 115-124. https://doi.org/10.1007/s10700-011-9100-y
[14] M. M. Lopes, F. S. Pedro Simões, L. C. Barros, et al., A fractional epidemiological model for COVID-19 using triangular norm, Mathware and Soft Computing: The Magazine of the European Society for Fuzzy Logic and Technology, 28(1) (2023), 115-133.
[15] M. M. Lopes, F. S. Pedro Simões, E. Esmi, L. C. Barros, The use of triangular norms in epidemiological models: A comparative study using COVID-19 data, IEEE Transactions on Fuzzy Systems, 31(5) (2023), 1542-1551. https: //doi.org/10.1109/TFUZZ.2022.3205357
[16] M. M. Lopes, F. Santo Pedro, L. C. Barros, et al., Use of T-norm in an epidemiological model for COVID-19, in: J. Rayz, V. Raskin, S. Dick, V. Kreinovich (eds.), Explainable AI and Other Applications of Fuzzy Techniques, NAFIPS 2021, Lecture Notes in Networks and Systems, 258, Springer, Cham, 2022. https://doi.org/10.1007/ 978-3-030-82099-2_23
[17] H. T. Nguyen, C. Walker, E. A. Walker, A first course in fuzzy logic, Chapman and Hall/CRC, 1999.
[18] W. Pedrycz, Some applicational aspects of fuzzy relational equations in system analysis, International Journal of General Systems, 9(3) (1983), 125-132. https://doi.org/https://doi.org/10.1080/03081078308960810
[19] F. Santo Pedro, L. C. Barros, The use of t-norms in mathematical models of epidemics, 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), (2013), 1-8. https://doi.org/10.1109/FUZZ-IEEE.2013.6622327
[20] V. F. Wasques, E. Esmi, L. C. Barros, B. Bede, Comparison between numerical solutions of fuzzy initial-value problems via interactive and standard arithmetic’s, in: Fuzzy Techniques: Theory and Applications, IFSA/NAFIPS 2019, Advances in Intelligent Systems and Computing, 1000, Springer, Cham, 2019. https://doi.org/10.1007/ 978-3-030-21920-8_62
[21] V. F. Wasques, E. Esmi, L. C. Barros, P. Sussner, Numerical solution for fuzzy initial value problems via interactive arithmetic: Application to chemical reactions, International Journal of Computational Intelligence Systems, 13(1) (2020), 1517-1529. https://doi.org/10.2991/ijcis.d.200916.001
[22] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences, 8(3) (1975), 199-249. https://doi.org/10.1016/0020-0255(75)90036-5 | ||
|
آمار تعداد مشاهده مقاله: 3 تعداد دریافت فایل اصل مقاله: 2 |
||