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A continuous-time dynamic fuzzy system with possibility transition is constructed and a differential of fuzzy states is given by paths. A limit theorem for fuzzy states is discussed under a contractive condition on fuzzy relations.
A dynamic fuzzy system defined on a compact state space is considered under a monotone property of the fuzzy relation. We study the limit of a sequence of fuzzy states and obtain a convergence theorem. The limit is characterized as the solution of a fuzzy relational equation. A numerical example is given to comprehend our idea in this paper.
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