A New Fuzzy Approach to Ordinary Differential Equations

In real-life problems, both parameters and data used in mathematical modeling are often vague or uncertain. In fields like system biology, diagnosis, image analysis, fault detection and many others, fuzzy differential equations and stochastic differential equations are an alternative to classical, or in the present context crisp, differential equations. The aim of the paper is to propose a new formulation of fuzzy ordinary differential equations for which the Hukuhara derivative is not needed. After a short review of recent results in the theory of ordered fuzzy numbers, an exemplary application to a dynamical system in mechanics is presented. Departing from the classical framework of dynamics, equations describing the fuzzy representation of the state are introduced and solved numerically for chosen fuzzy parameters and initial data.

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