Solutions to Fuzzy Differential Equations: Weakness and Possible Improvements

Witold Kosiński and Kurt Frischmuth

Keywords

Motion analysis, fuzzy differential equations, ordered fuzzy numbers

Abstract

We study and compare several approaches to ordinary differential equations for systems with a fuzzy state. Two ODE problems in 2D, the first linear, the second nonlinear, serve as examples to illustrate the concepts. We show that the existence of periodic solutions, which is given in the crisp case, is lost for fuzzy formulations. Possible improvement of the fuzzy approach by applying the concept of ordered fuzzy number theory as new generalization of convex fuzzy numbers, is proposed.

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