Towards the theory of fuzzy differential equations. (English) Zbl 1003.34046

Vorobiev, Dmitri; Seikkala, Seppo

Fuzzy Sets Syst. 125, No. 2, 231-237 (2002).

Here, the authors consider a comparative analysis of alternative approaches found in the existing literature, the common point of these approaches being the fact that they all avoid the use of fuzzy derivatives. Moreover, the authors devote to three new ideas in the theory of such “derivativeless” fuzzy differential equations.
Namely, they define the class of pyramidal fuzzy numbers and offer a new definition of the solution to fuzzy differential equations, the former belonging to the class of pyramidal fuzzy numbers.
For linear fuzzy systems, they use the Zadeh extension principle in order to build a closed-form fuzzy solution. This paper also contains an example, where they compare the fuzziness of a “pyramidal” solution to that one, which is derived by the extension principle.

Reviewer: Jong Yeoul Park (Pusan)

MSC:

34G20	Nonlinear differential equations in abstract spaces
47H04	Set-valued operators
47H14	Perturbations of nonlinear operators

Keywords:

fuzzy differential equations; fuzzy integro-differential equations; pyramidal fuzzy numbers; Zadeh extension principle; closed-form fuzzy solution

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