First order linear fuzzy differential equations under generalized differentiability

  • Authors:

  • Barnabás Bede;Imre J. Rudas;Attila L. Bencsik

  • Affiliations:

  • Department of Mechanical and System Engineering, Bánki Donát Faculty of Mechanical Engineering, Budapest Tech, Népszínház u. 8, H-1081 Budapest, Hungary and Department of ...;Department of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Budapest Tech, Bécsi út 96/B, H-1034 Budapest, Hungary;Department of Mechanical and System Engineering, Bánki Donát Faculty of Mechanical Engineering, Budapest Tech, Népszínház u. 8, H-1081 Budapest, Hungary

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

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Abstract

First order linear fuzzy differential equations are investigated. We interpret a fuzzy differential equation by using the strongly generalized differentiability concept, because under this interpretation, we may obtain solutions which have a decreasing length of their support (which means a decreasing uncertainty). In several applications the behaviour of these solutions better reflects the behaviour of some real-world systems. Derivatives of the H-difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations, using different versions of the variation of constants formula. Some examples show the rich behaviour of the solutions obtained.