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Fuzzy dynamical systems and the nature of their solutions. (English) Zbl 0591.34042
Fuzzy sets. Theory and applications to policy analysis and information systems, Proc. Symp., Durham/N.C. 1980, 93-121 (1980).

Summary: [For the entire collection see Zbl 0588.00004.]

The main thrust of this paper is to examine solutions to differential equations with fuzzy coefficients. Almost all problems in physics, engineering, biology, economics and other sciences to which mathematical methods are applicable are basically nondeterministic rather than deterministic. From the standpoint of applications, the modelling of such nondeterministic systems has been implemented via stochastic structures rather than fuzzy. It is thus the objective of this paper to give a careful presentation of the fuzzy approach to the solution of imprecise differential equations, by using the theory of fuzzy statistics, and to explore its applications to problems in science and engineering.

MSC:
37-99Dynamic systems and ergodic theory (MSC2000)