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A Geometric Approach to Solve Fuzzy Linear Systems of Differential Equations |
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PP: 484-499 |
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Author(s) |
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Nizami Gasilov,
S¸ ahin Emrah Amrahov,
Afet Golayo˘glu Fatullayev,
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Abstract |
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| In this paper, systems of linear differential equations with crisp real coefficients and
with initial condition described by a vector of fuzzy numbers are studied. A new
method based on geometric representations of linear transformations is proposed to
find a solution. The most important difference between this method and methods offered
in other papers is that the solution is considered to be a fuzzy set of real vectorfunctions
rather than a vector of fuzzy functions. Each member of the solution set
satisfies the given system with a certain possibility. It is shown that at any time the solution
constitutes a fuzzy region in the coordinate space, alpha-cuts of which are nested
parallelepipeds. The proposed method is illustrated on examples. |
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