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Fuzzy dynamical systems

Kloeden, P.E. (1982) Fuzzy dynamical systems. Fuzzy Sets and Systems, 7 (3). pp. 275-296.

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A fuzzy dynamical system on an underlying complete, locally compact metric state space X is defined axiomatically in terms of a fuzzy attainability set mapping on X. This definition includes as special cases crisp single and multivalued dynamical systems on X. It is shown that the support of such a fuzzy dynamical system on X is a crisp multivalued dynamical system on X, and that such a fuzzy dynamical system can be considered as a crisp dynamical system on a state space of nonempty compact fuzzy subsets of X. In addition fuzzy trajectories are defined, their existence established and various properties investigated.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Elsevier B.V.
Copyright: © 1982 Published by Elsevier B.V.
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