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Uncertainty propagation in linear fuzzy difference equations via Hamacher t-norms | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 23، شماره 6، بهمن و اسفند 2026، صفحه 17-37 اصل مقاله (540.14 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.53468.9464 | ||
| نویسندگان | ||
| V. F. Wasques* 1؛ J. D. 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 | ||
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