A Dynamic Center–Spread Framework for Uncertainty Propagation in Linear Fuzzy Differential Systems
DOI:
https://doi.org/10.65405/38erdk94Keywords:
Fuzzy differential equations; center–spread uncertainty; strongly generalized Hukuhara differentiability; uncertainty propagation; fuzzy Laplace representationAbstract
This paper proposes a dynamic center–spread framework for uncertainty propagation in linear fuzzy differential systems under strongly generalized Hukuhara (SGH) differentiability. The key novelty lies in treating the uncertainty magnitude as an independent dynamic variable, rather than deriving it indirectly from membership functions or -level sets. The uncertain state is represented as , where denotes the nominal trajectory and governs uncertainty evolution. The original fuzzy problem is decomposed into two independent deterministic equations: a center equation and a spread equation. Under standard continuity and Lipschitz conditions, existence and uniqueness of admissible solutions are established. The framework also introduces a center–spread Laplace representation by applying the classical Laplace transform separately to each component, and preserves consistency with the deterministic model when . Analytical examples and numerical experiments demonstrate the framework's ability to describe uncertainty attenuation and amplification independently of the nominal system behavior.
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