Elsevier

Fuzzy Sets and Systems

Volume 158, Issue 21, 1 November 2007, Pages 2339-2358
Fuzzy Sets and Systems

A class of linear differential dynamical systems with fuzzy initial condition

https://doi.org/10.1016/j.fss.2007.04.016Get rights and content

Abstract

This paper investigates linear first-order fuzzy differential dynamical systems where the initial condition is described by a fuzzy number. We use a complex number representation of the α-level sets of the fuzzy system and prove theorems that provide the solutions under such representation, which is applicable to practical computations and also has some implications for theory. Then the paper shows some properties of the two-dimensional dynamical systems, and their phase portraits are described by means of examples. There may be a significant difference between the solutions according to whether the matrix is nonnegative or not; finally, the paper points out future research on the fuzzy dynamical systems.

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    This work was supported by the National Science Foundation for Distinguished Young Scholars, PR China (Grant no. 70425005) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE of PR China (Grant no. 20023834-3).

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