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Minimal solution of fuzzy linear system of differential equations

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Abstract

In this paper, a new approach to solve the fuzzy linear system of differential equations based on pseudo-inverse is presented. In this work, we discuss the minimal solution of a system of linear fuzzy differential equations such as \(A\dot{x}(t)=B\dot{x}(t)+Cx(t), x(0)=x_0\) where A, B, and C are three real m  ×  n matrices and the initial condition x 0 is described by a vector made up of n fuzzy numbers. In this paper, we investigated a necessary and sufficient conditions for the existence fuzzy derivative \(\dot{x}(t)\) of a fuzzy process x(t) and a necessary and sufficient conditions for the minimal solution vector to be a fuzzy vector, given arbitrary input fuzzy vector x 0.

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Acknowledgments

We would like to offer our particular thanks to Dr. M. Eghbali for having edited this paper. We would also like to present our sincere thanks to the referees for their valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran

    Maryam Mosleh & Mahmood Otadi

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  1. Maryam Mosleh
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  2. Mahmood Otadi
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Correspondence to Maryam Mosleh.

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Mosleh, M., Otadi, M. Minimal solution of fuzzy linear system of differential equations. Neural Comput & Applic 21 (Suppl 1), 329–336 (2012). https://doi.org/10.1007/s00521-012-0913-6

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