Fuzzy differential equations and the extension principle

  • Authors:

  • M. T. Mizukoshi;L. C. Barros;Y. Chalco-Cano;H. Román-Flores;R. C. Bassanezi

  • Affiliations:

  • Institute of Mathematics and Statistics, Federal University of Goiás, 74001-970, Goiínia, GO, Brazil;Department of Applied Mathematics, IMECC, State University of Campinas, CP 6065, 13083-970, Campinas, SP, Brazil;Department of Mathematics, University of Tarapacá, Casilla 7D, Arica, Chile;Department of Mathematics, University of Tarapacá, Casilla 7D, Arica, Chile;Department of Applied Mathematics, IMECC, State University of Campinas, CP 6065, 13083-970, Campinas, SP, Brazil

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are the same. We also provide some illustrative examples.