Uncertainty propagation in linear fuzzy difference equations via Hamacher t-norms

Document Type : Original Manuscript

Authors

1 Ilum School of Science, Brazilian Center for Research in Energy and Materials, Campinas, Brazil

2 São Paulo State University, Rio Claro, Brazil

Abstract

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.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 6
November and December 2026
Pages 17-37

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